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101
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stringlengths 6
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https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | rw [map_fst_incrCounts_eq_cons_fst _ _ hout] | case cons.cons.inr.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
this : ¬x ∈ a.fst :: map Prod.fst as
⊢ length (uniqueAux xs (a.fst :: map Prod.fst (incrCounts as x))) =
length (uniqueAux xs (x :: a.fst :: map Prod.fst as)) | case cons.cons.inr.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
this : ¬x ∈ a.fst :: map Prod.fst as
⊢ length (uniqueAux xs (a.fst :: (map Prod.fst as ++ [x]))) = length (uniqueAux xs (x :: a.fst :: map Prod.fst as)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | apply List.length_uniqueAux_congr_append_cons_acc _ _ _ _ [] | case cons.cons.inr.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
this : ¬x ∈ a.fst :: map Prod.fst as
⊢ length (uniqueAux xs (a.fst :: (map Prod.fst as ++ [x]))) = length (uniqueAux xs (x :: a.fst :: map Prod.fst as)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | intros hneg | α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
⊢ ¬x ∈ a.fst :: map Prod.fst as | α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
hneg : x ∈ a.fst :: map Prod.fst as
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | cases hneg | α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
hneg : x ∈ a.fst :: map Prod.fst as
⊢ False | case head
α : Type u_1
inst✝ : DecidableEq α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = a.fst
hout : ¬a.fst ∈ map Prod.fst as
⊢ False
case tail
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
a✝ : Mem x (map Prod.fst as)
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | repeat contradiction | case head
α : Type u_1
inst✝ : DecidableEq α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = a.fst
hout : ¬a.fst ∈ map Prod.fst as
⊢ False
case tail
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
a✝ : Mem x (map Prod.fst as)
⊢ False | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | contradiction | case tail
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih :
∀ (acc : List (α × Nat)),
length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc))
a : α × Nat
as : List (α × Nat)
hfalse : ¬a.fst = x
hout : ¬x ∈ map Prod.fst as
a✝ : Mem x (map Prod.fst as)
⊢ False | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | induction xs with
| nil => simp [uniqueAux]
| cons x xs ih =>
intros as
cases Decidable.em (x ∈ as) with
| inl h =>
simp only [length, uniqueAux, h, ite_true]
apply Nat.le_trans
apply ih
rw [Nat.add_assoc, Nat.add_comm 1, ←Nat.add_assoc]
apply Nat.le_step
simp
| inr h =>
simp only [length, uniqueAux, h, ite_false]
apply Nat.le_trans
apply ih
simp only [length]
rw [Nat.add_comm _ 1, Nat.add_assoc]
apply Nat.le_refl | α : Type u_1
inst✝ : DecidableEq α
xs : List α
⊢ ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp [uniqueAux] | case nil
α : Type u_1
inst✝ : DecidableEq α
⊢ ∀ (as : List α), length (uniqueAux [] as) ≤ length [] + length as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | intros as | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
⊢ ∀ (as : List α), length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
⊢ length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | cases Decidable.em (x ∈ as) with
| inl h =>
simp only [length, uniqueAux, h, ite_true]
apply Nat.le_trans
apply ih
rw [Nat.add_assoc, Nat.add_comm 1, ←Nat.add_assoc]
apply Nat.le_step
simp
| inr h =>
simp only [length, uniqueAux, h, ite_false]
apply Nat.le_trans
apply ih
simp only [length]
rw [Nat.add_comm _ 1, Nat.add_assoc]
apply Nat.le_refl | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
⊢ length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp only [length, uniqueAux, h, ite_true] | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux xs as) ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply Nat.le_trans | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux xs as) ≤ length xs + 1 + length as | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux xs as) ≤ ?cons.inl.m
case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ ?cons.inl.m ≤ length xs + 1 + length as
case cons.inl.m
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ Nat |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply ih | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length (uniqueAux xs as) ≤ ?cons.inl.m
case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ ?cons.inl.m ≤ length xs + 1 + length as
case cons.inl.m
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ Nat | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | rw [Nat.add_assoc, Nat.add_comm 1, ←Nat.add_assoc] | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + 1 + length as | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + length as + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply Nat.le_step | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + length as + 1 | case cons.inl.a.h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp | case cons.inl.a.h
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : x ∈ as
⊢ length xs + length as ≤ length xs + length as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp only [length, uniqueAux, h, ite_false] | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux (x :: xs) as) ≤ length (x :: xs) + length as | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux xs (x :: as)) ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply Nat.le_trans | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux xs (x :: as)) ≤ length xs + 1 + length as | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux xs (x :: as)) ≤ ?cons.inr.m
case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ ?cons.inr.m ≤ length xs + 1 + length as
case cons.inr.m
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ Nat |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply ih | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length (uniqueAux xs (x :: as)) ≤ ?cons.inr.m
case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ ?cons.inr.m ≤ length xs + 1 + length as
case cons.inr.m
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ Nat | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + length (x :: as) ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | simp only [length] | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + length (x :: as) ≤ length xs + 1 + length as | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + (length as + 1) ≤ length xs + 1 + length as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | rw [Nat.add_comm _ 1, Nat.add_assoc] | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + (length as + 1) ≤ length xs + 1 + length as | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + (1 + length as) ≤ length xs + (1 + length as) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_le | [1817, 1] | [1837, 24] | apply Nat.le_refl | case cons.inr.a
α : Type u_1
inst✝ : DecidableEq α
x : α
xs : List α
ih : ∀ (as : List α), length (uniqueAux xs as) ≤ length xs + length as
as : List α
h : ¬x ∈ as
⊢ length xs + (1 + length as) ≤ length xs + (1 + length as) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | simp only [get, sieve] at * | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get (x :: xs) { val := Nat.succ n, isLt := pf1 } ∈ sieve (true :: bs) (x :: xs)
⊢ get (true :: bs) { val := Nat.succ n, isLt := pf2 } = true | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Iff.mp | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true | case self
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ ?a ↔ get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ ?a
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Prop |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply sieve_mem_iff_true_unique | case self
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ ?a ↔ get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ ?a
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Prop | case self.pf1
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ n < length ?self.xs
case self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Unique ?self.xs
case self.α
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Type u_1
case self.xs
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ List ?self.α
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get ?self.xs { val := n, isLt := ?self.pf1 } ∈ sieve bs ?self.xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . apply Nat.lt_of_succ_lt_succ pf1 | case self.pf1
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ n < length ?self.xs
case self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Unique ?self.xs
case self.α
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Type u_1
case self.xs
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ List ?self.α
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get ?self.xs { val := n, isLt := ?self.pf1 } ∈ sieve bs ?self.xs | case self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Unique xs
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get xs { val := n, isLt := (_ : n < length xs) } ∈ sieve bs xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . exact hu' | case self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Unique xs
case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get xs { val := n, isLt := (_ : n < length xs) } ∈ sieve bs xs | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get xs { val := n, isLt := (_ : n < length xs) } ∈ sieve bs xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . exact List.get_mem_cons_of_head_not_mem_getee hf hnmem | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get xs { val := n, isLt := (_ : n < length xs) } ∈ sieve bs xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Nat.lt_of_succ_lt_succ pf1 | case self.pf1
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ n < length ?self.xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | exact hu' | case self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ Unique xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | exact List.get_mem_cons_of_head_not_mem_getee hf hnmem | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hf : get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs
⊢ get xs { val := n, isLt := (_ : n < length xs) } ∈ sieve bs xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | simp only [get, sieve] at * | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get (true :: bs) { val := Nat.succ n, isLt := pf2 } = true
⊢ get (x :: xs) { val := Nat.succ n, isLt := pf1 } ∈ sieve (true :: bs) (x :: xs) | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Mem.tail | α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) } ∈ x :: sieve bs xs | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Mem (get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) }) (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Iff.mpr | case a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Mem (get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) }) (sieve bs xs) | case a.self
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Mem (get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) }) (sieve bs xs) ↔ ?a.b✝
case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ ?a.b✝
case a.b
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Prop |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply sieve_mem_iff_true_unique | case a.self
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Mem (get xs { val := n, isLt := (_ : Nat.succ n ≤ length xs) }) (sieve bs xs) ↔ ?a.b✝
case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ ?a.b✝
case a.b
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Prop | case a.self.pf2
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ n < length bs
case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Unique xs
case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := ?a.self.pf2✝ } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . apply Nat.lt_of_succ_lt_succ pf2 | case a.self.pf2
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ n < length bs
case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Unique xs
case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := ?a.self.pf2✝ } = true | case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Unique xs
case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := (_ : n < length bs) } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . exact hu' | case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Unique xs
case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := (_ : n < length bs) } = true | case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := (_ : n < length bs) } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | . exact hb | case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := (_ : n < length bs) } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | apply Nat.lt_of_succ_lt_succ pf2 | case a.self.pf2
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ n < length bs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | exact hu' | case a.self.hu
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ Unique xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_mem_iff_true_unique | [1867, 1] | [1905, 18] | exact hb | case a.a
α : Type u_1
n : Nat
x : α
xs : List α
bs : List Bool
pf1 : Nat.succ n < length (x :: xs)
pf2 : Nat.succ n < length (true :: bs)
hnmem : ¬x ∈ xs
hu' : Unique xs
hb : get bs { val := n, isLt := (_ : Nat.succ n ≤ length bs) } = true
⊢ get bs { val := n, isLt := (_ : n < length bs) } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | intro i xs bs pf1 pf2 f hu | α : Type u_1
β : Type u_2
⊢ ∀ {i : Nat} {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs) (f : α → β),
Unique (map f xs) →
(get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) ↔
get bs { val := i, isLt := pf2 } = true) | α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) ↔
get bs { val := i, isLt := pf2 } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Iff.intro | α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) ↔
get bs { val := i, isLt := pf2 } = true | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . intro hf
induction i generalizing xs bs with
| zero =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true => simp only [get, sieve] at *
| false =>
simp only [get, sieve] at *
exact mt mem_map_sieve_of_mem_map hnmem hf
| succ i ih =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. apply get_mem_cons_of_head_not_mem_getee hf hnmem
. apply Nat.lt_of_succ_lt_succ pf1
| false =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. exact hf
. apply Nat.lt_of_succ_lt_succ pf1 | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . intro hget
induction i generalizing xs bs with
| zero =>
match bs, xs with
| b :: bs, x :: xs =>
cases b with
| true => exact Mem.head _
| false => simp only [get, map] at hget
| succ i ih =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
apply Mem.tail
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget
| false =>
simp only [get, map, sieve] at *
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | intro hf | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
hf : get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := i, isLt := pf2 } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | induction i generalizing xs bs with
| zero =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true => simp only [get, sieve] at *
| false =>
simp only [get, sieve] at *
exact mt mem_map_sieve_of_mem_map hnmem hf
| succ i ih =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. apply get_mem_cons_of_head_not_mem_getee hf hnmem
. apply Nat.lt_of_succ_lt_succ pf1
| false =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. exact hf
. apply Nat.lt_of_succ_lt_succ pf1 | case mp
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
hf : get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := i, isLt := pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true => simp only [get, sieve] at *
| false =>
simp only [get, sieve] at *
exact mt mem_map_sieve_of_mem_map hnmem hf | case mp.zero
α : Type u_1
β : Type u_2
f : α → β
xs : List α
bs : List Bool
pf1 : Nat.zero < length xs
pf2 : Nat.zero < length bs
hu : Unique (map f xs)
hf : get (map f xs) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := Nat.zero, isLt := pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | cases b with
| true => simp only [get, sieve] at *
| false =>
simp only [get, sieve] at *
exact mt mem_map_sieve_of_mem_map hnmem hf | α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
b : Bool
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (b :: bs)
hf :
get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f (x :: xs))) } ∈
map f (sieve (b :: bs) (x :: xs))
⊢ get (b :: bs) { val := Nat.zero, isLt := pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve] at * | case true
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (true :: bs)
hf :
get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f (x :: xs))) } ∈
map f (sieve (true :: bs) (x :: xs))
⊢ get (true :: bs) { val := Nat.zero, isLt := pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve] at * | case false
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (false :: bs)
hf :
get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f (x :: xs))) } ∈
map f (sieve (false :: bs) (x :: xs))
⊢ get (false :: bs) { val := Nat.zero, isLt := pf2 } = true | case false
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (false :: bs)
hf : f x ∈ map f (sieve bs xs)
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact mt mem_map_sieve_of_mem_map hnmem hf | case false
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (false :: bs)
hf : f x ∈ map f (sieve bs xs)
⊢ False | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. apply get_mem_cons_of_head_not_mem_getee hf hnmem
. apply Nat.lt_of_succ_lt_succ pf1
| false =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. exact hf
. apply Nat.lt_of_succ_lt_succ pf1 | case mp.succ
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs : List α
bs : List Bool
pf1 : Nat.succ i < length xs
pf2 : Nat.succ i < length bs
hu : Unique (map f xs)
hf : get (map f xs) { val := Nat.succ i, isLt := (_ : Nat.succ i < length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := Nat.succ i, isLt := pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | cases b with
| true =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. apply get_mem_cons_of_head_not_mem_getee hf hnmem
. apply Nat.lt_of_succ_lt_succ pf1
| false =>
simp only [get, sieve, map] at *
apply ih
. exact hu
. exact hf
. apply Nat.lt_of_succ_lt_succ pf1 | α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
b : Bool
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (b :: bs)
hf :
get (map f (x :: xs)) { val := Nat.succ i, isLt := (_ : Nat.succ i < length (map f (x :: xs))) } ∈
map f (sieve (b :: bs) (x :: xs))
⊢ get (b :: bs) { val := Nat.succ i, isLt := pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve, map] at * | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf :
get (map f (x :: xs)) { val := Nat.succ i, isLt := (_ : Nat.succ i < length (map f (x :: xs))) } ∈
map f (sieve (true :: bs) (x :: xs))
⊢ get (true :: bs) { val := Nat.succ i, isLt := pf2 } = true | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply ih | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true | case true.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ Unique (map f ?true.xs)
case true.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ get (map f ?true.xs) { val := i, isLt := (_ : i < length (map f ?true.xs)) } ∈ map f (sieve bs ?true.xs)
case true.xs
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ List α
case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ i < length ?true.xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hu | case true.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ Unique (map f ?true.xs)
case true.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ get (map f ?true.xs) { val := i, isLt := (_ : i < length (map f ?true.xs)) } ∈ map f (sieve bs ?true.xs)
case true.xs
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ List α
case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ i < length ?true.xs | case true.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ i < length xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply get_mem_cons_of_head_not_mem_getee hf hnmem | case true.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ i < length xs | case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ i < length xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply Nat.lt_of_succ_lt_succ pf1 | case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ i < length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hu | case true.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ Unique (map f ?true.xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply get_mem_cons_of_head_not_mem_getee hf hnmem | case true.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Nat.lt_of_succ_lt_succ pf1 | case true.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs)
⊢ i < length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve, map] at * | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf :
get (map f (x :: xs)) { val := Nat.succ i, isLt := (_ : Nat.succ i < length (map f (x :: xs))) } ∈
map f (sieve (false :: bs) (x :: xs))
⊢ get (false :: bs) { val := Nat.succ i, isLt := pf2 } = true | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply ih | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ Unique (map f ?false.xs)
case false.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get (map f ?false.xs) { val := i, isLt := (_ : i < length (map f ?false.xs)) } ∈ map f (sieve bs ?false.xs)
case false.xs
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ List α
case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ i < length ?false.xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hu | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ Unique (map f ?false.xs)
case false.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get (map f ?false.xs) { val := i, isLt := (_ : i < length (map f ?false.xs)) } ∈ map f (sieve bs ?false.xs)
case false.xs
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ List α
case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ i < length ?false.xs | case false.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ i < length xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hf | case false.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ i < length xs | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ i < length xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply Nat.lt_of_succ_lt_succ pf1 | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ i < length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hu | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ Unique (map f ?false.xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hf | case false.hf
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Nat.lt_of_succ_lt_succ pf1 | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) →
get bs { val := i, isLt := pf2 } = true
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hf : get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs)
⊢ i < length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | intro hget | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
⊢ get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
hget : get bs { val := i, isLt := pf2 } = true
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | induction i generalizing xs bs with
| zero =>
match bs, xs with
| b :: bs, x :: xs =>
cases b with
| true => exact Mem.head _
| false => simp only [get, map] at hget
| succ i ih =>
match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
apply Mem.tail
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget
| false =>
simp only [get, map, sieve] at *
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget | case mpr
α : Type u_1
β : Type u_2
i : Nat
xs : List α
bs : List Bool
pf1 : i < length xs
pf2 : i < length bs
f : α → β
hu : Unique (map f xs)
hget : get bs { val := i, isLt := pf2 } = true
⊢ get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | match bs, xs with
| b :: bs, x :: xs =>
cases b with
| true => exact Mem.head _
| false => simp only [get, map] at hget | case mpr.zero
α : Type u_1
β : Type u_2
f : α → β
xs : List α
bs : List Bool
pf1 : Nat.zero < length xs
pf2 : Nat.zero < length bs
hu : Unique (map f xs)
hget : get bs { val := Nat.zero, isLt := pf2 } = true
⊢ get (map f xs) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | cases b with
| true => exact Mem.head _
| false => simp only [get, map] at hget | α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ : List Bool
b : Bool
bs : List Bool
x : α
xs : List α
pf1 : Nat.zero < length (x :: xs)
pf2 : Nat.zero < length (b :: bs)
hu : Unique (map f (x :: xs))
hget : get (b :: bs) { val := Nat.zero, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f (x :: xs))) } ∈
map f (sieve (b :: bs) (x :: xs)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact Mem.head _ | case true
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ bs : List Bool
x : α
xs : List α
pf1 : Nat.zero < length (x :: xs)
hu : Unique (map f (x :: xs))
pf2 : Nat.zero < length (true :: bs)
hget : get (true :: bs) { val := Nat.zero, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f (x :: xs))) } ∈
map f (sieve (true :: bs) (x :: xs)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, map] at hget | case false
α : Type u_1
β : Type u_2
f : α → β
xs✝ : List α
bs✝ bs : List Bool
x : α
xs : List α
pf1 : Nat.zero < length (x :: xs)
hu : Unique (map f (x :: xs))
pf2 : Nat.zero < length (false :: bs)
hget : get (false :: bs) { val := Nat.zero, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.zero, isLt := (_ : Nat.zero < length (map f (x :: xs))) } ∈
map f (sieve (false :: bs) (x :: xs)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | match bs, xs, hu with
| b :: bs, x :: xs, .cons hnmem hu =>
cases b with
| true =>
simp only [get, sieve, map] at *
apply Mem.tail
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget
| false =>
simp only [get, map, sieve] at *
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget | case mpr.succ
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs : List α
bs : List Bool
pf1 : Nat.succ i < length xs
pf2 : Nat.succ i < length bs
hu : Unique (map f xs)
hget : get bs { val := Nat.succ i, isLt := pf2 } = true
⊢ get (map f xs) { val := Nat.succ i, isLt := (_ : Nat.succ i < length (map f xs)) } ∈ map f (sieve bs xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | cases b with
| true =>
simp only [get, sieve, map] at *
apply Mem.tail
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget
| false =>
simp only [get, map, sieve] at *
apply ih
. apply Nat.lt_of_succ_lt_succ pf1
. exact hu
. exact hget | α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
b : Bool
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (b :: bs)
hget : get (b :: bs) { val := Nat.succ i, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.succ i, isLt := (_ : Nat.succ i < length (map f (x :: xs))) } ∈
map f (sieve (b :: bs) (x :: xs)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, sieve, map] at * | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get (true :: bs) { val := Nat.succ i, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.succ i, isLt := (_ : Nat.succ i < length (map f (x :: xs))) } ∈
map f (sieve (true :: bs) (x :: xs)) | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Mem.tail | case true
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ f x :: map f (sieve bs xs) | case true.a
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Mem (get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) }) (map f (sieve bs xs)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply ih | case true.a
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Mem (get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) }) (map f (sieve bs xs)) | case true.a.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length xs
case true.a.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs)
case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?true.a.pf2 } = true
case true.a.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply Nat.lt_of_succ_lt_succ pf1 | case true.a.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length xs
case true.a.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs)
case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?true.a.pf2 } = true
case true.a.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs | case true.a.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs)
case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?true.a.pf2 } = true
case true.a.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hu | case true.a.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs)
case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?true.a.pf2 } = true
case true.a.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs | case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?true.a.pf2 } = true
case true.a.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hget | case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?true.a.pf2 } = true
case true.a.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Nat.lt_of_succ_lt_succ pf1 | case true.a.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hu | case true.a.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hget | case true.a.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (true :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?true.a.pf2 } = true | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | simp only [get, map, sieve] at * | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get (false :: bs) { val := Nat.succ i, isLt := pf2 } = true
⊢ get (map f (x :: xs)) { val := Nat.succ i, isLt := (_ : Nat.succ i < length (map f (x :: xs))) } ∈
map f (sieve (false :: bs) (x :: xs)) | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply ih | case false
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get (map f xs) { val := i, isLt := (_ : Nat.succ i ≤ length (map f xs)) } ∈ map f (sieve bs xs) | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length xs
case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs)
case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?false.pf2 } = true
case false.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . apply Nat.lt_of_succ_lt_succ pf1 | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length xs
case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs)
case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?false.pf2 } = true
case false.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs)
case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?false.pf2 } = true
case false.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hu | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs)
case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?false.pf2 } = true
case false.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs | case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?false.pf2 } = true
case false.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | . exact hget | case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?false.pf2 } = true
case false.pf2
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length bs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | apply Nat.lt_of_succ_lt_succ pf1 | case false.pf1
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ i < length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hu | case false.hu
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ Unique (map f xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.sieve_map_mem_iff_true_unique | [1917, 1] | [1974, 21] | exact hget | case false.hget
α : Type u_1
β : Type u_2
f : α → β
i : Nat
ih :
∀ {xs : List α} {bs : List Bool} (pf1 : i < length xs) (pf2 : i < length bs),
Unique (map f xs) →
get bs { val := i, isLt := pf2 } = true →
get (map f xs) { val := i, isLt := (_ : i < length (map f xs)) } ∈ map f (sieve bs xs)
xs✝ : List α
bs✝ : List Bool
hu✝ : Unique (map f xs✝)
bs : List Bool
x : α
xs : List α
hnmem : ¬f x ∈ map f xs
hu : Unique (map f xs)
pf1 : Nat.succ i < length (x :: xs)
pf2 : Nat.succ i < length (false :: bs)
hget : get bs { val := i, isLt := (_ : Nat.succ i ≤ length bs) } = true
⊢ get bs { val := i, isLt := ?false.pf2 } = true | no goals |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | uIoo_of_le | [29, 1] | [30, 47] | rw [uIoo, inf_eq_left.2 h, sup_eq_right.2 h] | α : Type u_1
inst✝ : Lattice α
x y : α
h : x ≤ y
⊢ uIoo x y = Ioo x y | no goals |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | uIoo_of_ge | [32, 1] | [33, 47] | rw [uIoo, inf_eq_right.2 h, sup_eq_left.2 h] | α : Type u_1
inst✝ : Lattice α
x y : α
h : y ≤ x
⊢ uIoo x y = Ioo y x | no goals |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | uIoo_comm | [35, 1] | [35, 92] | rw [uIoo, uIoo, inf_comm, sup_comm] | α : Type u_1
inst✝ : Lattice α
x y : α
⊢ uIoo x y = uIoo y x | no goals |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | taylor_mean_remainder_unordered | [43, 1] | [71, 7] | rcases Ne.lt_or_lt hx with (hx₀ | hx₀) | f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (uIcc x₀ x)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (uIcc x₀ x)) (uIoo x₀ x)
gcont : ContinuousOn g (uIcc x₀ x)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
⊢ ∃ x',
∃ (_ : x' ∈ uIoo x₀ x),
f x - taylorWithinEval f n (uIcc x₀ x) x₀ x =
((x - x') ^ n / ↑n ! * (g x - g x₀) / g' x') • iteratedDerivWithin (n + 1) f (uIcc x₀ x) x' | case inl
f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (uIcc x₀ x)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (uIcc x₀ x)) (uIoo x₀ x)
gcont : ContinuousOn g (uIcc x₀ x)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
hx₀ : x₀ < x
⊢ ∃ x',
∃ (_ : x' ∈ uIoo x₀ x),
f x - taylorWithinEval f n (uIcc x₀ x) x₀ x =
((x - x') ^ n / ↑n ! * (g x - g x₀) / g' x') • iteratedDerivWithin (n + 1) f (uIcc x₀ x) x'
case inr
f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (uIcc x₀ x)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (uIcc x₀ x)) (uIoo x₀ x)
gcont : ContinuousOn g (uIcc x₀ x)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
hx₀ : x < x₀
⊢ ∃ x',
∃ (_ : x' ∈ uIoo x₀ x),
f x - taylorWithinEval f n (uIcc x₀ x) x₀ x =
((x - x') ^ n / ↑n ! * (g x - g x₀) / g' x') • iteratedDerivWithin (n + 1) f (uIcc x₀ x) x' |
https://github.com/b-mehta/ExponentialRamsey.git | 7e17b629a915a082869f494c8afa56a3e1c7a88d | ExponentialRamsey/Prereq/Mathlib/Analysis/Calculus/Taylor.lean | taylor_mean_remainder_unordered | [43, 1] | [71, 7] | rw [uIcc_of_ge hx₀.le] at hf hf' gcont ⊢ | case inr
f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (uIcc x₀ x)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (uIcc x₀ x)) (uIoo x₀ x)
gcont : ContinuousOn g (uIcc x₀ x)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
hx₀ : x < x₀
⊢ ∃ x',
∃ (_ : x' ∈ uIoo x₀ x),
f x - taylorWithinEval f n (uIcc x₀ x) x₀ x =
((x - x') ^ n / ↑n ! * (g x - g x₀) / g' x') • iteratedDerivWithin (n + 1) f (uIcc x₀ x) x' | case inr
f g g' : ℝ → ℝ
x x₀ : ℝ
n : ℕ
hx : x₀ ≠ x
hf : ContDiffOn ℝ (↑n) f (Icc x x₀)
hf' : DifferentiableOn ℝ (iteratedDerivWithin n f (Icc x x₀)) (uIoo x₀ x)
gcont : ContinuousOn g (Icc x x₀)
gdiff : ∀ x_1 ∈ uIoo x₀ x, HasDerivAt g (g' x_1) x_1
g'_ne : ∀ x_1 ∈ uIoo x₀ x, g' x_1 ≠ 0
hx₀ : x < x₀
⊢ ∃ x',
∃ (_ : x' ∈ uIoo x₀ x),
f x - taylorWithinEval f n (Icc x x₀) x₀ x =
((x - x') ^ n / ↑n ! * (g x - g x₀) / g' x') • iteratedDerivWithin (n + 1) f (Icc x x₀) x' |
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