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stringclasses 147
values | file_path
stringlengths 7
101
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stringlengths 1
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stringlengths 6
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| end
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https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_map_fst | [1651, 1] | [1661, 26] | simp only [hneq, ite_false, map, incrCounts] | α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
h' : Mem x (map Prod.fst as)
ih : map Prod.fst (incrCounts as x) = map Prod.fst as
hneq : ¬a.fst = x
⊢ map Prod.fst (incrCounts (a :: as) x) = map Prod.fst (a :: as) | α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
h' : Mem x (map Prod.fst as)
ih : map Prod.fst (incrCounts as x) = map Prod.fst as
hneq : ¬a.fst = x
⊢ a.fst :: map Prod.fst (incrCounts as x) = a.fst :: map Prod.fst as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_map_fst | [1651, 1] | [1661, 26] | exact congrArg _ ih | α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
h' : Mem x (map Prod.fst as)
ih : map Prod.fst (incrCounts as x) = map Prod.fst as
hneq : ¬a.fst = x
⊢ a.fst :: map Prod.fst (incrCounts as x) = a.fst :: map Prod.fst as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | intros as h | α : Type u_1
inst✝ : DecidableEq α
x : α
⊢ ∀ (as : List (α × Nat)), ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x] | α : Type u_1
inst✝ : DecidableEq α
x : α
as : List (α × Nat)
h : ¬x ∈ map Prod.fst as
⊢ map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | induction as with
| nil =>
simp only [incrCounts, map, HAppend.hAppend, Append.append, List.append]
| cons a as ih =>
simp only [map, incrCounts]
cases Decidable.em (a.1 = x) with
| inl heq =>
apply absurd h
apply not_not
simp only [map, heq]
apply List.Mem.head
| inr hneq =>
simp only [hneq, ite_false, map]
apply congrArg
apply ih
. intros hneg
apply h
apply List.Mem.tail _ hneg | α : Type u_1
inst✝ : DecidableEq α
x : α
as : List (α × Nat)
h : ¬x ∈ map Prod.fst as
⊢ map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | simp only [incrCounts, map, HAppend.hAppend, Append.append, List.append] | case nil
α : Type u_1
inst✝ : DecidableEq α
x : α
h : ¬x ∈ map Prod.fst []
⊢ map Prod.fst (incrCounts [] x) = map Prod.fst [] ++ [x] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | simp only [map, incrCounts] | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
⊢ map Prod.fst (incrCounts (a :: as) x) = map Prod.fst (a :: as) ++ [x] | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
⊢ map Prod.fst (if a.fst = x then (a.fst, a.snd + 1) :: as else (a.fst, a.snd) :: incrCounts as x) =
a.fst :: map Prod.fst as ++ [x] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | cases Decidable.em (a.1 = x) with
| inl heq =>
apply absurd h
apply not_not
simp only [map, heq]
apply List.Mem.head
| inr hneq =>
simp only [hneq, ite_false, map]
apply congrArg
apply ih
. intros hneg
apply h
apply List.Mem.tail _ hneg | case cons
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
⊢ map Prod.fst (if a.fst = x then (a.fst, a.snd + 1) :: as else (a.fst, a.snd) :: incrCounts as x) =
a.fst :: map Prod.fst as ++ [x] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | apply absurd h | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
heq : a.fst = x
⊢ map Prod.fst (if a.fst = x then (a.fst, a.snd + 1) :: as else (a.fst, a.snd) :: incrCounts as x) =
a.fst :: map Prod.fst as ++ [x] | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
heq : a.fst = x
⊢ ¬¬x ∈ map Prod.fst (a :: as) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | apply not_not | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
heq : a.fst = x
⊢ ¬¬x ∈ map Prod.fst (a :: as) | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
heq : a.fst = x
⊢ x ∈ map Prod.fst (a :: as) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | simp only [map, heq] | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
heq : a.fst = x
⊢ x ∈ map Prod.fst (a :: as) | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
heq : a.fst = x
⊢ x ∈ x :: map Prod.fst as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | apply List.Mem.head | case cons.inl.a
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
heq : a.fst = x
⊢ x ∈ x :: map Prod.fst as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | simp only [hneq, ite_false, map] | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
⊢ map Prod.fst (if a.fst = x then (a.fst, a.snd + 1) :: as else (a.fst, a.snd) :: incrCounts as x) =
a.fst :: map Prod.fst as ++ [x] | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
⊢ a.fst :: map Prod.fst (incrCounts as x) = a.fst :: map Prod.fst as ++ [x] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | apply congrArg | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
⊢ a.fst :: map Prod.fst (incrCounts as x) = a.fst :: map Prod.fst as ++ [x] | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
⊢ map Prod.fst (incrCounts as x) = List.append (map Prod.fst as) [x] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | apply ih | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
⊢ map Prod.fst (incrCounts as x) = List.append (map Prod.fst as) [x] | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
⊢ ¬x ∈ map Prod.fst as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | . intros hneg
apply h
apply List.Mem.tail _ hneg | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
⊢ ¬x ∈ map Prod.fst as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | intros hneg | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
⊢ ¬x ∈ map Prod.fst as | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
hneg : x ∈ map Prod.fst as
⊢ False |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | apply h | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
hneg : x ∈ map Prod.fst as
⊢ False | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
hneg : x ∈ map Prod.fst as
⊢ x ∈ map Prod.fst (a :: as) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.map_fst_incrCounts_eq_cons_fst | [1665, 1] | [1686, 35] | apply List.Mem.tail _ hneg | case cons.inr.h
α : Type u_1
inst✝ : DecidableEq α
x : α
a : α × Nat
as : List (α × Nat)
ih : ¬x ∈ map Prod.fst as → map Prod.fst (incrCounts as x) = map Prod.fst as ++ [x]
h : ¬x ∈ map Prod.fst (a :: as)
hneq : ¬a.fst = x
hneg : x ∈ map Prod.fst as
⊢ x ∈ map Prod.fst (a :: as) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | apply Iff.intro | α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ∨ x ∈ ys ↔ x ∈ xs ++ ys | case mp
α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ∨ x ∈ ys → x ∈ xs ++ ys
case mpr
α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ++ ys → x ∈ xs ∨ x ∈ ys |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | . intros hf
cases hf with
| inl hxs => apply mem_append_front _ _ _ hxs
| inr hys => apply mem_append_back _ _ _ hys | case mp
α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ∨ x ∈ ys → x ∈ xs ++ ys
case mpr
α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ++ ys → x ∈ xs ∨ x ∈ ys | case mpr
α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ++ ys → x ∈ xs ∨ x ∈ ys |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | . intros hb
induction xs with
| nil => exact Or.intro_right _ hb
| cons z xs ih =>
cases hb with
| head _ => apply Or.intro_left _ (List.Mem.head _)
| tail _ h' =>
cases ys with
| nil =>
apply Or.intro_left
apply List.Mem.tail
simp at h'
exact h'
| cons y ys =>
simp at h'
cases ih h' with
| inl hxxs =>
apply Or.intro_left
exact List.Mem.tail _ hxxs
| inr hxys =>
exact Or.intro_right _ hxys | case mpr
α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ++ ys → x ∈ xs ∨ x ∈ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | intros hf | case mp
α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ∨ x ∈ ys → x ∈ xs ++ ys | case mp
α : Type u_1
x : α
xs ys : List α
hf : x ∈ xs ∨ x ∈ ys
⊢ x ∈ xs ++ ys |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | cases hf with
| inl hxs => apply mem_append_front _ _ _ hxs
| inr hys => apply mem_append_back _ _ _ hys | case mp
α : Type u_1
x : α
xs ys : List α
hf : x ∈ xs ∨ x ∈ ys
⊢ x ∈ xs ++ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | apply mem_append_front _ _ _ hxs | case mp.inl
α : Type u_1
x : α
xs ys : List α
hxs : x ∈ xs
⊢ x ∈ xs ++ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | apply mem_append_back _ _ _ hys | case mp.inr
α : Type u_1
x : α
xs ys : List α
hys : x ∈ ys
⊢ x ∈ xs ++ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | intros hb | case mpr
α : Type u_1
x : α
xs ys : List α
⊢ x ∈ xs ++ ys → x ∈ xs ∨ x ∈ ys | case mpr
α : Type u_1
x : α
xs ys : List α
hb : x ∈ xs ++ ys
⊢ x ∈ xs ∨ x ∈ ys |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | induction xs with
| nil => exact Or.intro_right _ hb
| cons z xs ih =>
cases hb with
| head _ => apply Or.intro_left _ (List.Mem.head _)
| tail _ h' =>
cases ys with
| nil =>
apply Or.intro_left
apply List.Mem.tail
simp at h'
exact h'
| cons y ys =>
simp at h'
cases ih h' with
| inl hxxs =>
apply Or.intro_left
exact List.Mem.tail _ hxxs
| inr hxys =>
exact Or.intro_right _ hxys | case mpr
α : Type u_1
x : α
xs ys : List α
hb : x ∈ xs ++ ys
⊢ x ∈ xs ∨ x ∈ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | exact Or.intro_right _ hb | case mpr.nil
α : Type u_1
x : α
ys : List α
hb : x ∈ [] ++ ys
⊢ x ∈ [] ∨ x ∈ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | cases hb with
| head _ => apply Or.intro_left _ (List.Mem.head _)
| tail _ h' =>
cases ys with
| nil =>
apply Or.intro_left
apply List.Mem.tail
simp at h'
exact h'
| cons y ys =>
simp at h'
cases ih h' with
| inl hxxs =>
apply Or.intro_left
exact List.Mem.tail _ hxxs
| inr hxys =>
exact Or.intro_right _ hxys | case mpr.cons
α : Type u_1
x : α
ys : List α
z : α
xs : List α
ih : x ∈ xs ++ ys → x ∈ xs ∨ x ∈ ys
hb : x ∈ z :: xs ++ ys
⊢ x ∈ z :: xs ∨ x ∈ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | apply Or.intro_left _ (List.Mem.head _) | case mpr.cons.head
α : Type u_1
x : α
ys xs : List α
ih : x ∈ xs ++ ys → x ∈ xs ∨ x ∈ ys
⊢ x ∈ x :: xs ∨ x ∈ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | cases ys with
| nil =>
apply Or.intro_left
apply List.Mem.tail
simp at h'
exact h'
| cons y ys =>
simp at h'
cases ih h' with
| inl hxxs =>
apply Or.intro_left
exact List.Mem.tail _ hxxs
| inr hxys =>
exact Or.intro_right _ hxys | case mpr.cons.tail
α : Type u_1
x : α
ys : List α
z : α
xs : List α
ih : x ∈ xs ++ ys → x ∈ xs ∨ x ∈ ys
h' : Mem x (List.append xs ys)
⊢ x ∈ z :: xs ∨ x ∈ ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | apply Or.intro_left | case mpr.cons.tail.nil
α : Type u_1
x z : α
xs : List α
ih : x ∈ xs ++ [] → x ∈ xs ∨ x ∈ []
h' : Mem x (List.append xs [])
⊢ x ∈ z :: xs ∨ x ∈ [] | case mpr.cons.tail.nil.h
α : Type u_1
x z : α
xs : List α
ih : x ∈ xs ++ [] → x ∈ xs ∨ x ∈ []
h' : Mem x (List.append xs [])
⊢ x ∈ z :: xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | apply List.Mem.tail | case mpr.cons.tail.nil.h
α : Type u_1
x z : α
xs : List α
ih : x ∈ xs ++ [] → x ∈ xs ∨ x ∈ []
h' : Mem x (List.append xs [])
⊢ x ∈ z :: xs | case mpr.cons.tail.nil.h.a
α : Type u_1
x z : α
xs : List α
ih : x ∈ xs ++ [] → x ∈ xs ∨ x ∈ []
h' : Mem x (List.append xs [])
⊢ Mem x xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | simp at h' | case mpr.cons.tail.nil.h.a
α : Type u_1
x z : α
xs : List α
ih : x ∈ xs ++ [] → x ∈ xs ∨ x ∈ []
h' : Mem x (List.append xs [])
⊢ Mem x xs | case mpr.cons.tail.nil.h.a
α : Type u_1
x z : α
xs : List α
ih : x ∈ xs ++ [] → x ∈ xs ∨ x ∈ []
h' : Mem x xs
⊢ Mem x xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | exact h' | case mpr.cons.tail.nil.h.a
α : Type u_1
x z : α
xs : List α
ih : x ∈ xs ++ [] → x ∈ xs ∨ x ∈ []
h' : Mem x xs
⊢ Mem x xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | simp at h' | case mpr.cons.tail.cons
α : Type u_1
x z : α
xs : List α
y : α
ys : List α
ih : x ∈ xs ++ y :: ys → x ∈ xs ∨ x ∈ y :: ys
h' : Mem x (List.append xs (y :: ys))
⊢ x ∈ z :: xs ∨ x ∈ y :: ys | case mpr.cons.tail.cons
α : Type u_1
x z : α
xs : List α
y : α
ys : List α
ih : x ∈ xs ++ y :: ys → x ∈ xs ∨ x ∈ y :: ys
h' : Mem x (xs ++ y :: ys)
⊢ x ∈ z :: xs ∨ x ∈ y :: ys |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | cases ih h' with
| inl hxxs =>
apply Or.intro_left
exact List.Mem.tail _ hxxs
| inr hxys =>
exact Or.intro_right _ hxys | case mpr.cons.tail.cons
α : Type u_1
x z : α
xs : List α
y : α
ys : List α
ih : x ∈ xs ++ y :: ys → x ∈ xs ∨ x ∈ y :: ys
h' : Mem x (xs ++ y :: ys)
⊢ x ∈ z :: xs ∨ x ∈ y :: ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | apply Or.intro_left | case mpr.cons.tail.cons.inl
α : Type u_1
x z : α
xs : List α
y : α
ys : List α
ih : x ∈ xs ++ y :: ys → x ∈ xs ∨ x ∈ y :: ys
h' : Mem x (xs ++ y :: ys)
hxxs : x ∈ xs
⊢ x ∈ z :: xs ∨ x ∈ y :: ys | case mpr.cons.tail.cons.inl.h
α : Type u_1
x z : α
xs : List α
y : α
ys : List α
ih : x ∈ xs ++ y :: ys → x ∈ xs ∨ x ∈ y :: ys
h' : Mem x (xs ++ y :: ys)
hxxs : x ∈ xs
⊢ x ∈ z :: xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | exact List.Mem.tail _ hxxs | case mpr.cons.tail.cons.inl.h
α : Type u_1
x z : α
xs : List α
y : α
ys : List α
ih : x ∈ xs ++ y :: ys → x ∈ xs ∨ x ∈ y :: ys
h' : Mem x (xs ++ y :: ys)
hxxs : x ∈ xs
⊢ x ∈ z :: xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.mem_append_iff | [1693, 1] | [1720, 40] | exact Or.intro_right _ hxys | case mpr.cons.tail.cons.inr
α : Type u_1
x z : α
xs : List α
y : α
ys : List α
ih : x ∈ xs ++ y :: ys → x ∈ xs ∨ x ∈ y :: ys
h' : Mem x (xs ++ y :: ys)
hxys : x ∈ y :: ys
⊢ x ∈ z :: xs ∨ x ∈ y :: ys | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | induction xs generalizing cs with
| nil =>
simp [uniqueAux]
rw [←Nat.add_one,
Nat.add_assoc,
Nat.add_comm (length cs),
←Nat.add_assoc]
| cons z zs ih =>
have rearrange_mem :
(z ∈ cs ++ x :: (as ++ [y])) ↔ (z ∈ cs ++ y :: x :: as) := by
apply Iff.intro
. intros h
cases mem_append_iff.mpr h with
| inl hcs => exact List.mem_append_front _ _ _ hcs
| inr hcons =>
apply List.mem_append_back
rw [←cons_append] at hcons
cases mem_append_iff.mpr hcons with
| inl hxas => exact List.Mem.tail _ hxas
| inr hy =>
cases hy with
| tail _ _ => contradiction
| head _ => exact List.Mem.head _
. intros h
cases mem_append_iff.mpr h with
| inl hcs => exact List.mem_append_front _ _ _ hcs
| inr hcons =>
apply List.mem_append_back
cases hcons with
| head _ =>
apply List.Mem.tail
apply List.mem_append_back
apply (List.mem_singleton_iff y y).mpr rfl
| tail _ hcons' =>
rw [←cons_append]
exact List.mem_append_front _ _ _ hcons'
simp only [uniqueAux]
cases Decidable.em (z ∈ cs ++ x :: (as ++ [y])) with
| inl hin =>
simp only [hin, rearrange_mem.mp hin, ite_true]
apply ih
| inr hout =>
simp only [hout, rearrange_mem.not_iff_not_of_iff.mp hout, ite_false]
have rw_help (stuff) : (z :: (cs ++ stuff)) = ((z :: cs) ++ stuff) := rfl
rw [rw_help, rw_help]
apply ih | α : Type u_1
inst✝ : DecidableEq α
x y : α
as xs cs : List α
⊢ length (uniqueAux xs (cs ++ x :: (as ++ [y]))) = length (uniqueAux xs (cs ++ y :: x :: as)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | simp [uniqueAux] | case nil
α : Type u_1
inst✝ : DecidableEq α
x y : α
as cs : List α
⊢ length (uniqueAux [] (cs ++ x :: (as ++ [y]))) = length (uniqueAux [] (cs ++ y :: x :: as)) | case nil
α : Type u_1
inst✝ : DecidableEq α
x y : α
as cs : List α
⊢ Nat.succ (length as + Nat.succ 0 + length cs) = length as + Nat.succ 0 + Nat.succ 0 + length cs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | rw [←Nat.add_one,
Nat.add_assoc,
Nat.add_comm (length cs),
←Nat.add_assoc] | case nil
α : Type u_1
inst✝ : DecidableEq α
x y : α
as cs : List α
⊢ Nat.succ (length as + Nat.succ 0 + length cs) = length as + Nat.succ 0 + Nat.succ 0 + length cs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | have rearrange_mem :
(z ∈ cs ++ x :: (as ++ [y])) ↔ (z ∈ cs ++ y :: x :: as) := by
apply Iff.intro
. intros h
cases mem_append_iff.mpr h with
| inl hcs => exact List.mem_append_front _ _ _ hcs
| inr hcons =>
apply List.mem_append_back
rw [←cons_append] at hcons
cases mem_append_iff.mpr hcons with
| inl hxas => exact List.Mem.tail _ hxas
| inr hy =>
cases hy with
| tail _ _ => contradiction
| head _ => exact List.Mem.head _
. intros h
cases mem_append_iff.mpr h with
| inl hcs => exact List.mem_append_front _ _ _ hcs
| inr hcons =>
apply List.mem_append_back
cases hcons with
| head _ =>
apply List.Mem.tail
apply List.mem_append_back
apply (List.mem_singleton_iff y y).mpr rfl
| tail _ hcons' =>
rw [←cons_append]
exact List.mem_append_front _ _ _ hcons' | case cons
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ length (uniqueAux (z :: zs) (cs ++ x :: (as ++ [y]))) = length (uniqueAux (z :: zs) (cs ++ y :: x :: as)) | case cons
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
⊢ length (uniqueAux (z :: zs) (cs ++ x :: (as ++ [y]))) = length (uniqueAux (z :: zs) (cs ++ y :: x :: as)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | simp only [uniqueAux] | case cons
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
⊢ length (uniqueAux (z :: zs) (cs ++ x :: (as ++ [y]))) = length (uniqueAux (z :: zs) (cs ++ y :: x :: as)) | case cons
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
⊢ length
(if z ∈ cs ++ x :: (as ++ [y]) then uniqueAux zs (cs ++ x :: (as ++ [y]))
else uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) =
length
(if z ∈ cs ++ y :: x :: as then uniqueAux zs (cs ++ y :: x :: as) else uniqueAux zs (z :: (cs ++ y :: x :: as))) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | cases Decidable.em (z ∈ cs ++ x :: (as ++ [y])) with
| inl hin =>
simp only [hin, rearrange_mem.mp hin, ite_true]
apply ih
| inr hout =>
simp only [hout, rearrange_mem.not_iff_not_of_iff.mp hout, ite_false]
have rw_help (stuff) : (z :: (cs ++ stuff)) = ((z :: cs) ++ stuff) := rfl
rw [rw_help, rw_help]
apply ih | case cons
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
⊢ length
(if z ∈ cs ++ x :: (as ++ [y]) then uniqueAux zs (cs ++ x :: (as ++ [y]))
else uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) =
length
(if z ∈ cs ++ y :: x :: as then uniqueAux zs (cs ++ y :: x :: as) else uniqueAux zs (z :: (cs ++ y :: x :: as))) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | apply Iff.intro | α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as | case mp
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ x :: (as ++ [y]) → z ∈ cs ++ y :: x :: as
case mpr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ y :: x :: as → z ∈ cs ++ x :: (as ++ [y]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | . intros h
cases mem_append_iff.mpr h with
| inl hcs => exact List.mem_append_front _ _ _ hcs
| inr hcons =>
apply List.mem_append_back
rw [←cons_append] at hcons
cases mem_append_iff.mpr hcons with
| inl hxas => exact List.Mem.tail _ hxas
| inr hy =>
cases hy with
| tail _ _ => contradiction
| head _ => exact List.Mem.head _ | case mp
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ x :: (as ++ [y]) → z ∈ cs ++ y :: x :: as
case mpr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ y :: x :: as → z ∈ cs ++ x :: (as ++ [y]) | case mpr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ y :: x :: as → z ∈ cs ++ x :: (as ++ [y]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | . intros h
cases mem_append_iff.mpr h with
| inl hcs => exact List.mem_append_front _ _ _ hcs
| inr hcons =>
apply List.mem_append_back
cases hcons with
| head _ =>
apply List.Mem.tail
apply List.mem_append_back
apply (List.mem_singleton_iff y y).mpr rfl
| tail _ hcons' =>
rw [←cons_append]
exact List.mem_append_front _ _ _ hcons' | case mpr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ y :: x :: as → z ∈ cs ++ x :: (as ++ [y]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | intros h | case mp
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ x :: (as ++ [y]) → z ∈ cs ++ y :: x :: as | case mp
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
⊢ z ∈ cs ++ y :: x :: as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | cases mem_append_iff.mpr h with
| inl hcs => exact List.mem_append_front _ _ _ hcs
| inr hcons =>
apply List.mem_append_back
rw [←cons_append] at hcons
cases mem_append_iff.mpr hcons with
| inl hxas => exact List.Mem.tail _ hxas
| inr hy =>
cases hy with
| tail _ _ => contradiction
| head _ => exact List.Mem.head _ | case mp
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
⊢ z ∈ cs ++ y :: x :: as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | exact List.mem_append_front _ _ _ hcs | case mp.inl
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcs : z ∈ cs
⊢ z ∈ cs ++ y :: x :: as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | apply List.mem_append_back | case mp.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcons : z ∈ x :: (as ++ [y])
⊢ z ∈ cs ++ y :: x :: as | case mp.inr.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcons : z ∈ x :: (as ++ [y])
⊢ z ∈ y :: x :: as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | rw [←cons_append] at hcons | case mp.inr.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcons : z ∈ x :: (as ++ [y])
⊢ z ∈ y :: x :: as | case mp.inr.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcons : z ∈ x :: as ++ [y]
⊢ z ∈ y :: x :: as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | cases mem_append_iff.mpr hcons with
| inl hxas => exact List.Mem.tail _ hxas
| inr hy =>
cases hy with
| tail _ _ => contradiction
| head _ => exact List.Mem.head _ | case mp.inr.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcons : z ∈ x :: as ++ [y]
⊢ z ∈ y :: x :: as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | exact List.Mem.tail _ hxas | case mp.inr.a.inl
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcons : z ∈ x :: as ++ [y]
hxas : z ∈ x :: as
⊢ z ∈ y :: x :: as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | cases hy with
| tail _ _ => contradiction
| head _ => exact List.Mem.head _ | case mp.inr.a.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcons : z ∈ x :: as ++ [y]
hy : z ∈ [y]
⊢ z ∈ y :: x :: as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | contradiction | case mp.inr.a.inr.tail
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ x :: (as ++ [y])
hcons : z ∈ x :: as ++ [y]
a✝ : Mem z []
⊢ z ∈ y :: x :: as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | exact List.Mem.head _ | case mp.inr.a.inr.head
α : Type u_1
inst✝ : DecidableEq α
x y : α
as zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : y ∈ cs ++ x :: (as ++ [y])
hcons : y ∈ x :: as ++ [y]
⊢ y ∈ y :: x :: as | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | intros h | case mpr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
⊢ z ∈ cs ++ y :: x :: as → z ∈ cs ++ x :: (as ++ [y]) | case mpr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
⊢ z ∈ cs ++ x :: (as ++ [y]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | cases mem_append_iff.mpr h with
| inl hcs => exact List.mem_append_front _ _ _ hcs
| inr hcons =>
apply List.mem_append_back
cases hcons with
| head _ =>
apply List.Mem.tail
apply List.mem_append_back
apply (List.mem_singleton_iff y y).mpr rfl
| tail _ hcons' =>
rw [←cons_append]
exact List.mem_append_front _ _ _ hcons' | case mpr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
⊢ z ∈ cs ++ x :: (as ++ [y]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | exact List.mem_append_front _ _ _ hcs | case mpr.inl
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
hcs : z ∈ cs
⊢ z ∈ cs ++ x :: (as ++ [y]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | apply List.mem_append_back | case mpr.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
hcons : z ∈ y :: x :: as
⊢ z ∈ cs ++ x :: (as ++ [y]) | case mpr.inr.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
hcons : z ∈ y :: x :: as
⊢ z ∈ x :: (as ++ [y]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | cases hcons with
| head _ =>
apply List.Mem.tail
apply List.mem_append_back
apply (List.mem_singleton_iff y y).mpr rfl
| tail _ hcons' =>
rw [←cons_append]
exact List.mem_append_front _ _ _ hcons' | case mpr.inr.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
hcons : z ∈ y :: x :: as
⊢ z ∈ x :: (as ++ [y]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | apply List.Mem.tail | case mpr.inr.a.head
α : Type u_1
inst✝ : DecidableEq α
x y : α
as zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : y ∈ cs ++ y :: x :: as
⊢ y ∈ x :: (as ++ [y]) | case mpr.inr.a.head.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : y ∈ cs ++ y :: x :: as
⊢ Mem y (as ++ [y]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | apply List.mem_append_back | case mpr.inr.a.head.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : y ∈ cs ++ y :: x :: as
⊢ Mem y (as ++ [y]) | case mpr.inr.a.head.a.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : y ∈ cs ++ y :: x :: as
⊢ y ∈ [y] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | apply (List.mem_singleton_iff y y).mpr rfl | case mpr.inr.a.head.a.a
α : Type u_1
inst✝ : DecidableEq α
x y : α
as zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : y ∈ cs ++ y :: x :: as
⊢ y ∈ [y] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | rw [←cons_append] | case mpr.inr.a.tail
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
hcons' : Mem z (x :: as)
⊢ z ∈ x :: (as ++ [y]) | case mpr.inr.a.tail
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
hcons' : Mem z (x :: as)
⊢ z ∈ x :: as ++ [y] |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | exact List.mem_append_front _ _ _ hcons' | case mpr.inr.a.tail
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
h : z ∈ cs ++ y :: x :: as
hcons' : Mem z (x :: as)
⊢ z ∈ x :: as ++ [y] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | simp only [hin, rearrange_mem.mp hin, ite_true] | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hin : z ∈ cs ++ x :: (as ++ [y])
⊢ length
(if z ∈ cs ++ x :: (as ++ [y]) then uniqueAux zs (cs ++ x :: (as ++ [y]))
else uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) =
length
(if z ∈ cs ++ y :: x :: as then uniqueAux zs (cs ++ y :: x :: as) else uniqueAux zs (z :: (cs ++ y :: x :: as))) | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hin : z ∈ cs ++ x :: (as ++ [y])
⊢ length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | apply ih | case cons.inl
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hin : z ∈ cs ++ x :: (as ++ [y])
⊢ length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | simp only [hout, rearrange_mem.not_iff_not_of_iff.mp hout, ite_false] | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hout : ¬z ∈ cs ++ x :: (as ++ [y])
⊢ length
(if z ∈ cs ++ x :: (as ++ [y]) then uniqueAux zs (cs ++ x :: (as ++ [y]))
else uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) =
length
(if z ∈ cs ++ y :: x :: as then uniqueAux zs (cs ++ y :: x :: as) else uniqueAux zs (z :: (cs ++ y :: x :: as))) | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hout : ¬z ∈ cs ++ x :: (as ++ [y])
⊢ length (uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) = length (uniqueAux zs (z :: (cs ++ y :: x :: as))) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | have rw_help (stuff) : (z :: (cs ++ stuff)) = ((z :: cs) ++ stuff) := rfl | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hout : ¬z ∈ cs ++ x :: (as ++ [y])
⊢ length (uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) = length (uniqueAux zs (z :: (cs ++ y :: x :: as))) | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hout : ¬z ∈ cs ++ x :: (as ++ [y])
rw_help : ∀ (stuff : List α), z :: (cs ++ stuff) = z :: cs ++ stuff
⊢ length (uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) = length (uniqueAux zs (z :: (cs ++ y :: x :: as))) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | rw [rw_help, rw_help] | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hout : ¬z ∈ cs ++ x :: (as ++ [y])
rw_help : ∀ (stuff : List α), z :: (cs ++ stuff) = z :: cs ++ stuff
⊢ length (uniqueAux zs (z :: (cs ++ x :: (as ++ [y])))) = length (uniqueAux zs (z :: (cs ++ y :: x :: as))) | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hout : ¬z ∈ cs ++ x :: (as ++ [y])
rw_help : ∀ (stuff : List α), z :: (cs ++ stuff) = z :: cs ++ stuff
⊢ length (uniqueAux zs (z :: cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (z :: cs ++ y :: x :: as)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_uniqueAux_congr_append_cons_acc | [1722, 1] | [1772, 15] | apply ih | case cons.inr
α : Type u_1
inst✝ : DecidableEq α
x y : α
as : List α
z : α
zs : List α
ih : ∀ (cs : List α), length (uniqueAux zs (cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (cs ++ y :: x :: as))
cs : List α
rearrange_mem : z ∈ cs ++ x :: (as ++ [y]) ↔ z ∈ cs ++ y :: x :: as
hout : ¬z ∈ cs ++ x :: (as ++ [y])
rw_help : ∀ (stuff : List α), z :: (cs ++ stuff) = z :: cs ++ stuff
⊢ length (uniqueAux zs (z :: cs ++ x :: (as ++ [y]))) = length (uniqueAux zs (z :: cs ++ y :: x :: as)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | induction xs generalizing acc with
| nil => simp [foldl, uniqueAux]
| cons x xs ih =>
simp only [uniqueAux, foldl]
cases acc with
| nil =>
simp only [incrCounts, map, List.not_mem_nil, ite_false]
apply ih
| cons a as =>
simp only [incrCounts]
cases Decidable.em (a.1 = x) with
| inl htrue =>
simp only [htrue, ite_true, incrCounts, map]
rw [if_pos]
. apply ih
. exact List.Mem.head _
| inr hfalse =>
simp only [hfalse, ite_false, incrCounts, map]
rw [ih]
cases Decidable.em (x ∈ map Prod.fst as) with
| inl hin =>
have : x ∈ a.1 :: map Prod.fst as := List.Mem.tail _ hin
simp only [this, ite_true, map, uniqueAux]
apply congrArg
apply congrArg
apply congrArg
exact map_fst_incrCounts_eq_map_fst x as hin
| inr hout =>
have : ¬ (x ∈ a.1 :: map Prod.fst as) := by
intros hneg; cases hneg; repeat contradiction
simp only [this, ite_false, map]
rw [map_fst_incrCounts_eq_cons_fst _ _ hout]
apply List.length_uniqueAux_congr_append_cons_acc _ _ _ _ [] | α : Type u_1
inst✝ : DecidableEq α
xs : List α
acc : List (α × Nat)
⊢ length (foldl (fun acc v => incrCounts acc v) acc xs) = length (uniqueAux xs (map Prod.fst acc)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | simp [foldl, uniqueAux] | case nil
α : Type u_1
inst✝ : DecidableEq α
acc : List (α × Nat)
⊢ length (foldl (fun acc v => incrCounts acc v) acc []) = length (uniqueAux [] (map Prod.fst acc)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | simp only [uniqueAux, foldl] | case cons
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))
acc : List (α × Nat)
⊢ length (foldl (fun acc v => incrCounts acc v) acc (x :: xs)) = length (uniqueAux (x :: xs) (map Prod.fst acc)) | case cons
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))
acc : List (α × Nat)
⊢ length (foldl (fun acc v => incrCounts acc v) (incrCounts acc x) xs) =
length (if x ∈ map Prod.fst acc then uniqueAux xs (map Prod.fst acc) else uniqueAux xs (x :: map Prod.fst acc)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | cases acc with
| nil =>
simp only [incrCounts, map, List.not_mem_nil, ite_false]
apply ih
| cons a as =>
simp only [incrCounts]
cases Decidable.em (a.1 = x) with
| inl htrue =>
simp only [htrue, ite_true, incrCounts, map]
rw [if_pos]
. apply ih
. exact List.Mem.head _
| inr hfalse =>
simp only [hfalse, ite_false, incrCounts, map]
rw [ih]
cases Decidable.em (x ∈ map Prod.fst as) with
| inl hin =>
have : x ∈ a.1 :: map Prod.fst as := List.Mem.tail _ hin
simp only [this, ite_true, map, uniqueAux]
apply congrArg
apply congrArg
apply congrArg
exact map_fst_incrCounts_eq_map_fst x as hin
| inr hout =>
have : ¬ (x ∈ a.1 :: map Prod.fst as) := by
intros hneg; cases hneg; repeat contradiction
simp only [this, ite_false, map]
rw [map_fst_incrCounts_eq_cons_fst _ _ hout]
apply List.length_uniqueAux_congr_append_cons_acc _ _ _ _ [] | case cons
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))
acc : List (α × Nat)
⊢ length (foldl (fun acc v => incrCounts acc v) (incrCounts acc x) xs) =
length (if x ∈ map Prod.fst acc then uniqueAux xs (map Prod.fst acc) else uniqueAux xs (x :: map Prod.fst acc)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | simp only [incrCounts, map, List.not_mem_nil, ite_false] | case cons.nil
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))
⊢ length (foldl (fun acc v => incrCounts acc v) (incrCounts [] x) xs) =
length (if x ∈ map Prod.fst [] then uniqueAux xs (map Prod.fst []) else uniqueAux xs (x :: map Prod.fst [])) | case cons.nil
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))
⊢ length (foldl (fun acc v => incrCounts acc v) [(x, 1)] xs) = length (uniqueAux xs [x]) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | apply ih | case cons.nil
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))
⊢ length (foldl (fun acc v => incrCounts acc v) [(x, 1)] xs) = length (uniqueAux xs [x]) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | simp only [incrCounts] | case cons.cons
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)
⊢ length (foldl (fun acc v => incrCounts acc v) (incrCounts (a :: as) x) xs) =
length
(if x ∈ map Prod.fst (a :: as) then uniqueAux xs (map Prod.fst (a :: as))
else uniqueAux xs (x :: map Prod.fst (a :: as))) | case cons.cons
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)
⊢ length
(foldl (fun acc v => incrCounts acc v)
(if a.fst = x then (a.fst, a.snd + 1) :: as else (a.fst, a.snd) :: incrCounts as x) xs) =
length
(if x ∈ map Prod.fst (a :: as) then uniqueAux xs (map Prod.fst (a :: as))
else uniqueAux xs (x :: map Prod.fst (a :: as))) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | cases Decidable.em (a.1 = x) with
| inl htrue =>
simp only [htrue, ite_true, incrCounts, map]
rw [if_pos]
. apply ih
. exact List.Mem.head _
| inr hfalse =>
simp only [hfalse, ite_false, incrCounts, map]
rw [ih]
cases Decidable.em (x ∈ map Prod.fst as) with
| inl hin =>
have : x ∈ a.1 :: map Prod.fst as := List.Mem.tail _ hin
simp only [this, ite_true, map, uniqueAux]
apply congrArg
apply congrArg
apply congrArg
exact map_fst_incrCounts_eq_map_fst x as hin
| inr hout =>
have : ¬ (x ∈ a.1 :: map Prod.fst as) := by
intros hneg; cases hneg; repeat contradiction
simp only [this, ite_false, map]
rw [map_fst_incrCounts_eq_cons_fst _ _ hout]
apply List.length_uniqueAux_congr_append_cons_acc _ _ _ _ [] | case cons.cons
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)
⊢ length
(foldl (fun acc v => incrCounts acc v)
(if a.fst = x then (a.fst, a.snd + 1) :: as else (a.fst, a.snd) :: incrCounts as x) xs) =
length
(if x ∈ map Prod.fst (a :: as) then uniqueAux xs (map Prod.fst (a :: as))
else uniqueAux xs (x :: map Prod.fst (a :: as))) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | simp only [htrue, ite_true, incrCounts, map] | case cons.cons.inl
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)
htrue : a.fst = x
⊢ length
(foldl (fun acc v => incrCounts acc v)
(if a.fst = x then (a.fst, a.snd + 1) :: as else (a.fst, a.snd) :: incrCounts as x) xs) =
length
(if x ∈ map Prod.fst (a :: as) then uniqueAux xs (map Prod.fst (a :: as))
else uniqueAux xs (x :: map Prod.fst (a :: as))) | case cons.cons.inl
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)
htrue : a.fst = x
⊢ length (foldl (fun acc v => incrCounts acc v) ((x, a.snd + 1) :: as) xs) =
length
(if x ∈ x :: map Prod.fst as then uniqueAux xs (x :: map Prod.fst as)
else uniqueAux xs (x :: x :: map Prod.fst as)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | rw [if_pos] | case cons.cons.inl
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)
htrue : a.fst = x
⊢ length (foldl (fun acc v => incrCounts acc v) ((x, a.snd + 1) :: as) xs) =
length
(if x ∈ x :: map Prod.fst as then uniqueAux xs (x :: map Prod.fst as)
else uniqueAux xs (x :: x :: map Prod.fst as)) | case cons.cons.inl
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)
htrue : a.fst = x
⊢ length (foldl (fun acc v => incrCounts acc v) ((x, a.snd + 1) :: as) xs) =
length (uniqueAux xs (x :: map Prod.fst as))
case cons.cons.inl.hc
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)
htrue : a.fst = x
⊢ x ∈ x :: map Prod.fst as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | . apply ih | case cons.cons.inl
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)
htrue : a.fst = x
⊢ length (foldl (fun acc v => incrCounts acc v) ((x, a.snd + 1) :: as) xs) =
length (uniqueAux xs (x :: map Prod.fst as))
case cons.cons.inl.hc
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)
htrue : a.fst = x
⊢ x ∈ x :: map Prod.fst as | case cons.cons.inl.hc
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)
htrue : a.fst = x
⊢ x ∈ x :: map Prod.fst as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | . exact List.Mem.head _ | case cons.cons.inl.hc
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)
htrue : a.fst = x
⊢ x ∈ x :: 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] | apply ih | case cons.cons.inl
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)
htrue : a.fst = x
⊢ length (foldl (fun acc v => incrCounts acc v) ((x, a.snd + 1) :: as) xs) =
length (uniqueAux xs (x :: 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] | exact List.Mem.head _ | case cons.cons.inl.hc
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)
htrue : a.fst = x
⊢ x ∈ x :: 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] | simp only [hfalse, ite_false, incrCounts, map] | case cons.cons.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
⊢ length
(foldl (fun acc v => incrCounts acc v)
(if a.fst = x then (a.fst, a.snd + 1) :: as else (a.fst, a.snd) :: incrCounts as x) xs) =
length
(if x ∈ map Prod.fst (a :: as) then uniqueAux xs (map Prod.fst (a :: as))
else uniqueAux xs (x :: map Prod.fst (a :: as))) | case cons.cons.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
⊢ length (foldl (fun acc v => incrCounts acc v) ((a.fst, a.snd) :: incrCounts as x) xs) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else 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] | rw [ih] | case cons.cons.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
⊢ length (foldl (fun acc v => incrCounts acc v) ((a.fst, a.snd) :: incrCounts as x) xs) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else uniqueAux xs (x :: a.fst :: map Prod.fst as)) | case cons.cons.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
⊢ length (uniqueAux xs (map Prod.fst ((a.fst, a.snd) :: incrCounts as x))) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else 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] | cases Decidable.em (x ∈ map Prod.fst as) with
| inl hin =>
have : x ∈ a.1 :: map Prod.fst as := List.Mem.tail _ hin
simp only [this, ite_true, map, uniqueAux]
apply congrArg
apply congrArg
apply congrArg
exact map_fst_incrCounts_eq_map_fst x as hin
| inr hout =>
have : ¬ (x ∈ a.1 :: map Prod.fst as) := by
intros hneg; cases hneg; repeat contradiction
simp only [this, ite_false, map]
rw [map_fst_incrCounts_eq_cons_fst _ _ hout]
apply List.length_uniqueAux_congr_append_cons_acc _ _ _ _ [] | case cons.cons.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
⊢ length (uniqueAux xs (map Prod.fst ((a.fst, a.snd) :: incrCounts as x))) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else 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] | have : x ∈ a.1 :: map Prod.fst as := List.Mem.tail _ hin | case cons.cons.inr.inl
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
hin : x ∈ map Prod.fst as
⊢ length (uniqueAux xs (map Prod.fst ((a.fst, a.snd) :: incrCounts as x))) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else uniqueAux xs (x :: a.fst :: map Prod.fst as)) | case cons.cons.inr.inl
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
hin : x ∈ map Prod.fst as
this : x ∈ a.fst :: map Prod.fst as
⊢ length (uniqueAux xs (map Prod.fst ((a.fst, a.snd) :: incrCounts as x))) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else 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] | simp only [this, ite_true, map, uniqueAux] | case cons.cons.inr.inl
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
hin : x ∈ map Prod.fst as
this : x ∈ a.fst :: map Prod.fst as
⊢ length (uniqueAux xs (map Prod.fst ((a.fst, a.snd) :: incrCounts as x))) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else uniqueAux xs (x :: a.fst :: map Prod.fst as)) | case cons.cons.inr.inl
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
hin : 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 (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 congrArg | case cons.cons.inr.inl
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
hin : 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 (a.fst :: map Prod.fst as)) | case cons.cons.inr.inl.h
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
hin : x ∈ map Prod.fst as
this : x ∈ a.fst :: map Prod.fst as
⊢ uniqueAux xs (a.fst :: map Prod.fst (incrCounts as x)) = uniqueAux xs (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 congrArg | case cons.cons.inr.inl.h
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
hin : x ∈ map Prod.fst as
this : x ∈ a.fst :: map Prod.fst as
⊢ uniqueAux xs (a.fst :: map Prod.fst (incrCounts as x)) = uniqueAux xs (a.fst :: map Prod.fst as) | case cons.cons.inr.inl.h.h
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
hin : x ∈ map Prod.fst as
this : x ∈ a.fst :: map Prod.fst as
⊢ a.fst :: map Prod.fst (incrCounts as 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 congrArg | case cons.cons.inr.inl.h.h
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
hin : x ∈ map Prod.fst as
this : x ∈ a.fst :: map Prod.fst as
⊢ a.fst :: map Prod.fst (incrCounts as x) = a.fst :: map Prod.fst as | case cons.cons.inr.inl.h.h.h
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
hin : x ∈ map Prod.fst as
this : x ∈ a.fst :: map Prod.fst as
⊢ map Prod.fst (incrCounts as x) = map Prod.fst as |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_counts_aux | [1774, 1] | [1810, 71] | exact map_fst_incrCounts_eq_map_fst x as hin | case cons.cons.inr.inl.h.h.h
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
hin : x ∈ map Prod.fst as
this : x ∈ a.fst :: map Prod.fst as
⊢ map Prod.fst (incrCounts as x) = 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] | have : ¬ (x ∈ a.1 :: map Prod.fst as) := by
intros hneg; cases hneg; repeat contradiction | 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
⊢ length (uniqueAux xs (map Prod.fst ((a.fst, a.snd) :: incrCounts as x))) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else 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 (map Prod.fst ((a.fst, a.snd) :: incrCounts as x))) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else 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] | simp only [this, ite_false, map] | 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 (map Prod.fst ((a.fst, a.snd) :: incrCounts as x))) =
length
(if x ∈ a.fst :: map Prod.fst as then uniqueAux xs (a.fst :: map Prod.fst as)
else 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 (incrCounts as x))) =
length (uniqueAux xs (x :: a.fst :: map Prod.fst as)) |
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