url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
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| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
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| state_after
stringlengths 6
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https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/SchemaFunctions.lean | Schema.lookupType_nths_eq_lookupType | [372, 1] | [413, 28] | conv =>
lhs
simp only [Schema.nths, Schema.map, htoprove, Schema.lookupType] | η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
nm : η
hnths : HasName nm (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
hhnm : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns)
h : hasNameEqHeadOrTail hnths = Sum.inr hhnm
htoprove : hnths = HasName.tl hhnm
⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) { fst := nm, snd := hnths } =
lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName hhnm } | η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
nm : η
hnths : HasName nm (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
hhnm : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns)
h : hasNameEqHeadOrTail hnths = Sum.inr hhnm
htoprove : hnths = HasName.tl hhnm
⊢ lookupType (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns)
{ fst := nm, snd := hhnm } =
lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName hhnm } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/SchemaFunctions.lean | Schema.lookupType_nths_eq_lookupType | [372, 1] | [413, 28] | apply lookupType_nths_eq_lookupType | η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
nm : η
hnths : HasName nm (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
hhnm : HasName nm (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns)
h : hasNameEqHeadOrTail hnths = Sum.inr hhnm
htoprove : hnths = HasName.tl hhnm
⊢ lookupType (map (fun n => nth ((snm, sτ) :: sch) n.val (_ : n.val < length ((snm, sτ) :: sch))) ns)
{ fst := nm, snd := hhnm } =
lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName hhnm } | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/SchemaFunctions.lean | Schema.lookupType_nths_eq_lookupType | [372, 1] | [413, 28] | cases heqt | η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
nm : η
hnths : HasName nm (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
heqt : (nth sch n (_ : Nat.succ n ≤ length sch)).fst ≡ nm
h : hasNameEqHeadOrTail hnths = Sum.inl heqt
⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns)) { fst := nm, snd := hnths } =
lookupType ((snm, sτ) :: sch) { fst := nm, snd := hasNameOfNthsHasName hnths } | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hnths } =
lookupType ((snm, sτ) :: sch)
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hasNameOfNthsHasName hnths } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/SchemaFunctions.lean | Schema.lookupType_nths_eq_lookupType | [372, 1] | [413, 28] | have htoprove : hnths = .hd :=
Schema.hasNameEqHeadOrTail_inl hnths (EqT.ofEq h) | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hnths } =
lookupType ((snm, sτ) :: sch)
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hasNameOfNthsHasName hnths } | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hnths } =
lookupType ((snm, sτ) :: sch)
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hasNameOfNthsHasName hnths } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/SchemaFunctions.lean | Schema.lookupType_nths_eq_lookupType | [372, 1] | [413, 28] | simp only [Schema.nths, Schema.map, Schema.lookupType, htoprove] | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ lookupType (nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hnths } =
lookupType ((snm, sτ) :: sch)
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hasNameOfNthsHasName hnths } | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ (nth sch n (_ : Nat.succ n ≤ length sch)).snd =
lookupType ((snm, sτ) :: sch)
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hasNameOfNthsHasName HasName.hd } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/SchemaFunctions.lean | Schema.lookupType_nths_eq_lookupType | [372, 1] | [413, 28] | unfold Schema.hasNameOfNthsHasName | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ (nth sch n (_ : Nat.succ n ≤ length sch)).snd =
lookupType ((snm, sτ) :: sch)
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst, snd := hasNameOfNthsHasName HasName.hd } | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ (nth sch n (_ : Nat.succ n ≤ length sch)).snd =
lookupType ((snm, sτ) :: sch)
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst,
snd :=
match (nth sch n (_ : Nat.succ n ≤ length sch)).fst, hasNameEqHeadOrTail HasName.hd, HasName.hd with
|
.((nth ((snm, sτ) :: sch) { val := Nat.succ n, isLt := pf }.val
(_ : { val := Nat.succ n, isLt := pf }.val < length ((snm, sτ) :: sch))).fst),
Sum.inl
(EqT.refl
.((nth ((snm, sτ) :: sch) { val := Nat.succ n, isLt := pf }.val
(_ : { val := Nat.succ n, isLt := pf }.val < length ((snm, sτ) :: sch))).fst)),
h => hasNthName { val := Nat.succ n, isLt := pf }
| hdr, Sum.inr hhnm, h => hasNameOfNthsHasName hhnm } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/SchemaFunctions.lean | Schema.lookupType_nths_eq_lookupType | [372, 1] | [413, 28] | simp only [Schema.hasNameEqHeadOrTail, Schema.hasNthName, Schema.lookupType] | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ (nth sch n (_ : Nat.succ n ≤ length sch)).snd =
lookupType ((snm, sτ) :: sch)
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst,
snd :=
match (nth sch n (_ : Nat.succ n ≤ length sch)).fst, hasNameEqHeadOrTail HasName.hd, HasName.hd with
|
.((nth ((snm, sτ) :: sch) { val := Nat.succ n, isLt := pf }.val
(_ : { val := Nat.succ n, isLt := pf }.val < length ((snm, sτ) :: sch))).fst),
Sum.inl
(EqT.refl
.((nth ((snm, sτ) :: sch) { val := Nat.succ n, isLt := pf }.val
(_ : { val := Nat.succ n, isLt := pf }.val < length ((snm, sτ) :: sch))).fst)),
h => hasNthName { val := Nat.succ n, isLt := pf }
| hdr, Sum.inr hhnm, h => hasNameOfNthsHasName hhnm } | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ (nth sch n (_ : Nat.succ n ≤ length sch)).snd =
lookupType sch
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst,
snd := hasNthName { val := n, isLt := (_ : n < length sch) } } |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/SchemaFunctions.lean | Schema.lookupType_nths_eq_lookupType | [372, 1] | [413, 28] | apply Schema.lookup_nth | case refl
η : Type u_η
dec_η : DecidableEq η
schema : Schema
snm : η
sτ : Type u_1
sch : List Header
n : Nat
pf : Nat.succ n < length ((snm, sτ) :: sch)
ns : List (Fin (length ((snm, sτ) :: sch)))
hnths :
HasName (nth sch n (_ : Nat.succ n ≤ length sch)).fst
(nths ((snm, sτ) :: sch) ({ val := Nat.succ n, isLt := pf } :: ns))
h : hasNameEqHeadOrTail hnths = Sum.inl (EqT.refl (nth sch n (_ : Nat.succ n ≤ length sch)).fst)
htoprove : hnths = HasName.hd
⊢ (nth sch n (_ : Nat.succ n ≤ length sch)).snd =
lookupType sch
{ fst := (nth sch n (_ : Nat.succ n ≤ length sch)).fst,
snd := hasNthName { val := n, isLt := (_ : n < length sch) } } | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | Nat.add_lt_add_of_lt | [56, 1] | [63, 13] | intros a m n h | ⊢ ∀ (a m n : Nat), m < n → m + a < n + a | a m n : Nat
h : m < n
⊢ m + a < n + a |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | Nat.add_lt_add_of_lt | [56, 1] | [63, 13] | induction a with
| zero => exact h
| succ n' ih =>
rw [←Nat.add_one, ←Nat.add_assoc, ←Nat.add_assoc, Nat.add_one, Nat.add_one]
apply Nat.succ_lt_succ
exact ih | a m n : Nat
h : m < n
⊢ m + a < n + a | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | Nat.add_lt_add_of_lt | [56, 1] | [63, 13] | exact h | case zero
m n : Nat
h : m < n
⊢ m + zero < n + zero | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | Nat.add_lt_add_of_lt | [56, 1] | [63, 13] | rw [←Nat.add_one, ←Nat.add_assoc, ←Nat.add_assoc, Nat.add_one, Nat.add_one] | case succ
m n : Nat
h : m < n
n' : Nat
ih : m + n' < n + n'
⊢ m + succ n' < n + succ n' | case succ
m n : Nat
h : m < n
n' : Nat
ih : m + n' < n + n'
⊢ succ (m + n') < succ (n + n') |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | Nat.add_lt_add_of_lt | [56, 1] | [63, 13] | apply Nat.succ_lt_succ | case succ
m n : Nat
h : m < n
n' : Nat
ih : m + n' < n + n'
⊢ succ (m + n') < succ (n + n') | case succ.a
m n : Nat
h : m < n
n' : Nat
ih : m + n' < n + n'
⊢ m + n' < n + n' |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | Nat.add_lt_add_of_lt | [56, 1] | [63, 13] | exact ih | case succ.a
m n : Nat
h : m < n
n' : Nat
ih : m + n' < n + n'
⊢ m + n' < n + n' | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | induction xs with
| nil =>
intro rs
simp only [filter, filterTR.loop]
rw [List.length_reverse]
simp only [length, Nat.zero_add]
apply Nat.le.refl
| cons x xs ih =>
intro rs
simp only [filter, filterTR.loop]
cases (g x) with
| true => simp only
apply Nat.le_trans (ih (x::rs))
simp only [length]
rw [Nat.add_comm (length rs), Nat.add_assoc]
apply Nat.le.refl
| false => simp only [length]
apply Nat.le_trans (ih rs)
rw [Nat.add_comm (length xs) 1,
Nat.add_assoc 1,
Nat.add_comm 1,
Nat.add_one]
apply Nat.le.step
apply Nat.le.refl | α : Type u_1
g : α → Bool
xs : List α
⊢ ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | intro rs | case nil
α : Type u_1
g : α → Bool
⊢ ∀ (rs : List α), length (filterTR.loop g [] rs) ≤ length [] + length rs | case nil
α : Type u_1
g : α → Bool
rs : List α
⊢ length (filterTR.loop g [] rs) ≤ length [] + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | simp only [filter, filterTR.loop] | case nil
α : Type u_1
g : α → Bool
rs : List α
⊢ length (filterTR.loop g [] rs) ≤ length [] + length rs | case nil
α : Type u_1
g : α → Bool
rs : List α
⊢ length (reverse rs) ≤ length [] + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | rw [List.length_reverse] | case nil
α : Type u_1
g : α → Bool
rs : List α
⊢ length (reverse rs) ≤ length [] + length rs | case nil
α : Type u_1
g : α → Bool
rs : List α
⊢ length rs ≤ length [] + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | simp only [length, Nat.zero_add] | case nil
α : Type u_1
g : α → Bool
rs : List α
⊢ length rs ≤ length [] + length rs | case nil
α : Type u_1
g : α → Bool
rs : List α
⊢ length rs ≤ length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | apply Nat.le.refl | case nil
α : Type u_1
g : α → Bool
rs : List α
⊢ length rs ≤ length rs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | intro rs | case cons
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
⊢ ∀ (rs : List α), length (filterTR.loop g (x :: xs) rs) ≤ length (x :: xs) + length rs | case cons
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length (filterTR.loop g (x :: xs) rs) ≤ length (x :: xs) + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | simp only [filter, filterTR.loop] | case cons
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length (filterTR.loop g (x :: xs) rs) ≤ length (x :: xs) + length rs | case cons
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length
(match g x with
| true => filterTR.loop g xs (x :: rs)
| false => filterTR.loop g xs rs) ≤
length (x :: xs) + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | cases (g x) with
| true => simp only
apply Nat.le_trans (ih (x::rs))
simp only [length]
rw [Nat.add_comm (length rs), Nat.add_assoc]
apply Nat.le.refl
| false => simp only [length]
apply Nat.le_trans (ih rs)
rw [Nat.add_comm (length xs) 1,
Nat.add_assoc 1,
Nat.add_comm 1,
Nat.add_one]
apply Nat.le.step
apply Nat.le.refl | case cons
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length
(match g x with
| true => filterTR.loop g xs (x :: rs)
| false => filterTR.loop g xs rs) ≤
length (x :: xs) + length rs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | simp only | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length
(match true with
| true => filterTR.loop g xs (x :: rs)
| false => filterTR.loop g xs rs) ≤
length (x :: xs) + length rs | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length (filterTR.loop g xs (x :: rs)) ≤ length (x :: xs) + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | apply Nat.le_trans (ih (x::rs)) | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length (filterTR.loop g xs (x :: rs)) ≤ length (x :: xs) + length rs | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + length (x :: rs) ≤ length (x :: xs) + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | simp only [length] | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + length (x :: rs) ≤ length (x :: xs) + length rs | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + (length rs + 1) ≤ length xs + 1 + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | rw [Nat.add_comm (length rs), Nat.add_assoc] | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + (length rs + 1) ≤ length xs + 1 + length rs | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + (1 + length rs) ≤ length xs + (1 + length rs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | apply Nat.le.refl | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + (1 + length rs) ≤ length xs + (1 + length rs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | simp only [length] | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length
(match false with
| true => filterTR.loop g xs (x :: rs)
| false => filterTR.loop g xs rs) ≤
length (x :: xs) + length rs | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length (filterTR.loop g xs rs) ≤ length xs + 1 + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | apply Nat.le_trans (ih rs) | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length (filterTR.loop g xs rs) ≤ length xs + 1 + length rs | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + length rs ≤ length xs + 1 + length rs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | rw [Nat.add_comm (length xs) 1,
Nat.add_assoc 1,
Nat.add_comm 1,
Nat.add_one] | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + length rs ≤ length xs + 1 + length rs | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + length rs ≤ Nat.succ (length xs + length rs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | apply Nat.le.step | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ length xs + length rs ≤ Nat.succ (length xs + length rs) | case cons.false.a
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ Nat.le (length xs + length rs) (length xs + length rs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_filterTR_le | [149, 1] | [176, 33] | apply Nat.le.refl | case cons.false.a
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : ∀ (rs : List α), length (filterTR.loop g xs rs) ≤ length xs + length rs
rs : List α
⊢ Nat.le (length xs + length rs) (length xs + length rs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | induction xs with
| nil => simp [length]
| cons x xs ih =>
simp only [filter]
cases (g x) with
| true =>
simp only
apply Nat.succ_le_succ
exact ih
| false =>
simp only
apply Nat.le.step
exact ih | α : Type u_1
g : α → Bool
xs : List α
⊢ length (filter g xs) ≤ length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | simp [length] | case nil
α : Type u_1
g : α → Bool
⊢ length (filter g []) ≤ length [] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | simp only [filter] | case cons
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length (filter g (x :: xs)) ≤ length (x :: xs) | case cons
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length
(match g x with
| true => x :: filter g xs
| false => filter g xs) ≤
length (x :: xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | cases (g x) with
| true =>
simp only
apply Nat.succ_le_succ
exact ih
| false =>
simp only
apply Nat.le.step
exact ih | case cons
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length
(match g x with
| true => x :: filter g xs
| false => filter g xs) ≤
length (x :: xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | simp only | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length
(match true with
| true => x :: filter g xs
| false => filter g xs) ≤
length (x :: xs) | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length (x :: filter g xs) ≤ length (x :: xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | apply Nat.succ_le_succ | case cons.true
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length (x :: filter g xs) ≤ length (x :: xs) | case cons.true.a
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length (filter g xs) ≤ length xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | exact ih | case cons.true.a
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length (filter g xs) ≤ length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | simp only | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length
(match false with
| true => x :: filter g xs
| false => filter g xs) ≤
length (x :: xs) | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length (filter g xs) ≤ length (x :: xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | apply Nat.le.step | case cons.false
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ length (filter g xs) ≤ length (x :: xs) | case cons.false.a
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ Nat.le (length (filter g xs)) (length xs) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_length | [178, 1] | [192, 17] | exact ih | case cons.false.a
α : Type u_1
g : α → Bool
x : α
xs : List α
ih : length (filter g xs) ≤ length xs
⊢ Nat.le (length (filter g xs)) (length xs) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst' | [203, 1] | [212, 14] | simp only [split, length] | α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).fst ≤ length xs
⊢ length (split (x₁ :: x₂ :: xs)).fst ≤ length (x₁ :: x₂ :: xs) | α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).fst ≤ length xs
⊢ length (split xs).fst + 1 ≤ length xs + 1 + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst' | [203, 1] | [212, 14] | apply Nat.le.step | α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).fst ≤ length xs
⊢ length (split xs).fst + 1 ≤ length xs + 1 + 1 | case a
α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).fst ≤ length xs
⊢ Nat.le (length (split xs).fst + 1) (length xs + 1) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst' | [203, 1] | [212, 14] | apply Nat.succ_le_succ | case a
α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).fst ≤ length xs
⊢ Nat.le (length (split xs).fst + 1) (length xs + 1) | case a.a
α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).fst ≤ length xs
⊢ length (split xs).fst ≤ length xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst' | [203, 1] | [212, 14] | apply ih | case a.a
α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).fst ≤ length xs
⊢ length (split xs).fst ≤ length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst | [214, 1] | [229, 24] | simp only [split, length] | α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length (x :: x' :: xs) ≤ 1 ∨ length (split (x :: x' :: xs)).fst < length (x :: x' :: xs)
⊢ length (x₁ :: x₂ :: x :: x' :: xs) ≤ 1 ∨
length (split (x₁ :: x₂ :: x :: x' :: xs)).fst < length (x₁ :: x₂ :: x :: x' :: xs) | α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length (x :: x' :: xs) ≤ 1 ∨ length (split (x :: x' :: xs)).fst < length (x :: x' :: xs)
⊢ length xs + 1 + 1 + 1 + 1 ≤ 1 ∨ length (split xs).fst + 1 + 1 < length xs + 1 + 1 + 1 + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst | [214, 1] | [229, 24] | apply Or.intro_right | α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length (x :: x' :: xs) ≤ 1 ∨ length (split (x :: x' :: xs)).fst < length (x :: x' :: xs)
⊢ length xs + 1 + 1 + 1 + 1 ≤ 1 ∨ length (split xs).fst + 1 + 1 < length xs + 1 + 1 + 1 + 1 | case h
α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length (x :: x' :: xs) ≤ 1 ∨ length (split (x :: x' :: xs)).fst < length (x :: x' :: xs)
⊢ length (split xs).fst + 1 + 1 < length xs + 1 + 1 + 1 + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst | [214, 1] | [229, 24] | apply Nat.succ_lt_succ | case h
α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length (x :: x' :: xs) ≤ 1 ∨ length (split (x :: x' :: xs)).fst < length (x :: x' :: xs)
⊢ length (split xs).fst + 1 + 1 < length xs + 1 + 1 + 1 + 1 | case h.a
α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length (x :: x' :: xs) ≤ 1 ∨ length (split (x :: x' :: xs)).fst < length (x :: x' :: xs)
⊢ length (split xs).fst + 1 < length xs + 3 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst | [214, 1] | [229, 24] | simp [length, Nat.add] at ih | case h.a
α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length (x :: x' :: xs) ≤ 1 ∨ length (split (x :: x' :: xs)).fst < length (x :: x' :: xs)
⊢ length (split xs).fst + 1 < length xs + 3 | case h.a
α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length xs + 1 + 1 ≤ 1 ∨ length (split xs).fst + 1 < length xs + 1 + 1
⊢ length (split xs).fst + 1 < length xs + 3 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst | [214, 1] | [229, 24] | apply Nat.lt.step | case h.a
α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length xs + 1 + 1 ≤ 1 ∨ length (split xs).fst + 1 < length xs + 1 + 1
⊢ length (split xs).fst + 1 < length xs + 3 | case h.a.a
α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length xs + 1 + 1 ≤ 1 ∨ length (split xs).fst + 1 < length xs + 1 + 1
⊢ length (split xs).fst + 1 < length xs + 2 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst | [214, 1] | [229, 24] | cases ih with
| inl _ => contradiction
| inr h => apply h | case h.a.a
α : Type u_1
x₁ x₂ x x' : α
xs : List α
ih : length xs + 1 + 1 ≤ 1 ∨ length (split xs).fst + 1 < length xs + 1 + 1
⊢ length (split xs).fst + 1 < length xs + 2 | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst | [214, 1] | [229, 24] | contradiction | case h.a.a.inl
α : Type u_1
x₁ x₂ x x' : α
xs : List α
h✝ : length xs + 1 + 1 ≤ 1
⊢ length (split xs).fst + 1 < length xs + 2 | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_fst | [214, 1] | [229, 24] | apply h | case h.a.a.inr
α : Type u_1
x₁ x₂ x x' : α
xs : List α
h : length (split xs).fst + 1 < length xs + 1 + 1
⊢ length (split xs).fst + 1 < length xs + 2 | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd | [231, 1] | [243, 14] | simp only [split, length] | α : Type u_1
x₁ x₂ x : α
xs : List α
ih : x :: xs = [] ∨ length (split (x :: xs)).snd < length (x :: xs)
⊢ x₁ :: x₂ :: x :: xs = [] ∨ length (split (x₁ :: x₂ :: x :: xs)).snd < length (x₁ :: x₂ :: x :: xs) | α : Type u_1
x₁ x₂ x : α
xs : List α
ih : x :: xs = [] ∨ length (split (x :: xs)).snd < length (x :: xs)
⊢ False ∨ length (split (x :: xs)).snd + 1 < length xs + 1 + 1 + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd | [231, 1] | [243, 14] | apply Or.intro_right | α : Type u_1
x₁ x₂ x : α
xs : List α
ih : x :: xs = [] ∨ length (split (x :: xs)).snd < length (x :: xs)
⊢ False ∨ length (split (x :: xs)).snd + 1 < length xs + 1 + 1 + 1 | case h
α : Type u_1
x₁ x₂ x : α
xs : List α
ih : x :: xs = [] ∨ length (split (x :: xs)).snd < length (x :: xs)
⊢ length (split (x :: xs)).snd + 1 < length xs + 1 + 1 + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd | [231, 1] | [243, 14] | apply Nat.succ_lt_succ | case h
α : Type u_1
x₁ x₂ x : α
xs : List α
ih : x :: xs = [] ∨ length (split (x :: xs)).snd < length (x :: xs)
⊢ length (split (x :: xs)).snd + 1 < length xs + 1 + 1 + 1 | case h.a
α : Type u_1
x₁ x₂ x : α
xs : List α
ih : x :: xs = [] ∨ length (split (x :: xs)).snd < length (x :: xs)
⊢ length (split (x :: xs)).snd < length xs + 2 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd | [231, 1] | [243, 14] | simp at ih | case h.a
α : Type u_1
x₁ x₂ x : α
xs : List α
ih : x :: xs = [] ∨ length (split (x :: xs)).snd < length (x :: xs)
⊢ length (split (x :: xs)).snd < length xs + 2 | case h.a
α : Type u_1
x₁ x₂ x : α
xs : List α
ih : length (split (x :: xs)).snd < Nat.succ (length xs)
⊢ length (split (x :: xs)).snd < length xs + 2 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd | [231, 1] | [243, 14] | apply Nat.lt.step | case h.a
α : Type u_1
x₁ x₂ x : α
xs : List α
ih : length (split (x :: xs)).snd < Nat.succ (length xs)
⊢ length (split (x :: xs)).snd < length xs + 2 | case h.a.a
α : Type u_1
x₁ x₂ x : α
xs : List α
ih : length (split (x :: xs)).snd < Nat.succ (length xs)
⊢ length (split (x :: xs)).snd < length xs + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd | [231, 1] | [243, 14] | apply ih | case h.a.a
α : Type u_1
x₁ x₂ x : α
xs : List α
ih : length (split (x :: xs)).snd < Nat.succ (length xs)
⊢ length (split (x :: xs)).snd < length xs + 1 | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd' | [245, 1] | [254, 14] | simp only [split, length] | α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).snd ≤ length xs
⊢ length (split (x₁ :: x₂ :: xs)).snd ≤ length (x₁ :: x₂ :: xs) | α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).snd ≤ length xs
⊢ length (split xs).snd + 1 ≤ length xs + 1 + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd' | [245, 1] | [254, 14] | apply Nat.le.step | α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).snd ≤ length xs
⊢ length (split xs).snd + 1 ≤ length xs + 1 + 1 | case a
α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).snd ≤ length xs
⊢ Nat.le (length (split xs).snd + 1) (length xs + 1) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd' | [245, 1] | [254, 14] | apply Nat.succ_le_succ | case a
α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).snd ≤ length xs
⊢ Nat.le (length (split xs).snd + 1) (length xs + 1) | case a.a
α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).snd ≤ length xs
⊢ length (split xs).snd ≤ length xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.split_length_snd' | [245, 1] | [254, 14] | apply ih | case a.a
α : Type u_1
x₁ x₂ : α
xs : List α
ih : length (split xs).snd ≤ length xs
⊢ length (split xs).snd ≤ length xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.zip_length_eq_of_length_eq | [312, 1] | [322, 29] | simp only [List.length] at h | α : Type u_1
β : Type u_2
x : α
xs : List α
y : β
ys : List β
h : length (x :: xs) = length (y :: ys)
⊢ length xs = length ys | α : Type u_1
β : Type u_2
x : α
xs : List α
y : β
ys : List β
h : length xs + 1 = length ys + 1
⊢ length xs = length ys |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.zip_length_eq_of_length_eq | [312, 1] | [322, 29] | apply Nat.succ.inj | α : Type u_1
β : Type u_2
x : α
xs : List α
y : β
ys : List β
h : length xs + 1 = length ys + 1
⊢ length xs = length ys | case x
α : Type u_1
β : Type u_2
x : α
xs : List α
y : β
ys : List β
h : length xs + 1 = length ys + 1
⊢ Nat.succ (length xs) = Nat.succ (length ys) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.zip_length_eq_of_length_eq | [312, 1] | [322, 29] | apply h | case x
α : Type u_1
β : Type u_2
x : α
xs : List α
y : β
ys : List β
h : length xs + 1 = length ys + 1
⊢ Nat.succ (length xs) = Nat.succ (length ys) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | simp [prod, length] | α : Type u_1
β : Type u_2
x✝ : List β
⊢ length (prod [] x✝) = length [] * length x✝ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | simp [prod, length] | α : Type u_1
β : Type u_2
x : α
xs : List α
⊢ length (prod (x :: xs) []) = length (x :: xs) * length [] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | simp only [prod] | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ length (prod [x] (y :: ys)) = length [x] * length (y :: ys) | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ length ((x, y) :: prod [x] ys) = length [x] * length (y :: ys) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | unfold length | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ length ((x, y) :: prod [x] ys) = length [x] * length (y :: ys) | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ length (prod [x] ys) + 1 = (length [] + 1) * (length ys + 1) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | rw [ih] | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ length (prod [x] ys) + 1 = (length [] + 1) * (length ys + 1) | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ length [x] * length ys + 1 = (length [] + 1) * (length ys + 1) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | simp only [length] | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ length [x] * length ys + 1 = (length [] + 1) * (length ys + 1) | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ (0 + 1) * length ys + 1 = (0 + 1) * (length ys + 1) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | rw [Nat.one_mul, Nat.one_mul] | α : Type u_1
β : Type u_2
x : α
y : β
ys : List β
ih : length (prod [x] ys) = length [x] * length ys
⊢ (0 + 1) * length ys + 1 = (0 + 1) * (length ys + 1) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | apply Nat.add_lt_add_of_lt | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
⊢ Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys) | case a
α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
⊢ Nat.succ 0 < Nat.succ (Nat.succ (length xs)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | apply Nat.succ_lt_succ $ Nat.succ_pos (length xs) | case a
α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
⊢ Nat.succ 0 < Nat.succ (Nat.succ (length xs)) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | apply Nat.add_lt_add_of_lt | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
⊢ Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys) | case a
α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
⊢ Nat.succ (length xs) < Nat.succ (Nat.succ (length xs)) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | apply Nat.succ_lt_succ | case a
α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
⊢ Nat.succ (length xs) < Nat.succ (Nat.succ (length xs)) | case a.a
α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
⊢ length xs < length xs + 1 |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | apply Nat.lt.base | case a.a
α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
⊢ length xs < length xs + 1 | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | unfold prod | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ length (prod (x :: x' :: xs) (y :: ys)) = length (x :: x' :: xs) * length (y :: ys) | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ length
(let_fun h₁ := (_ : Nat.succ 0 + length (y :: ys) < Nat.succ (Nat.succ (length xs)) + length (y :: ys));
let_fun h₂ := (_ : Nat.succ (length xs) + length (y :: ys) < Nat.succ (Nat.succ (length xs)) + length (y :: ys));
prod [x] (y :: ys) ++ prod (x' :: xs) (y :: ys)) =
length (x :: x' :: xs) * length (y :: ys) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | simp only | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ length
(let_fun h₁ := (_ : Nat.succ 0 + length (y :: ys) < Nat.succ (Nat.succ (length xs)) + length (y :: ys));
let_fun h₂ := (_ : Nat.succ (length xs) + length (y :: ys) < Nat.succ (Nat.succ (length xs)) + length (y :: ys));
prod [x] (y :: ys) ++ prod (x' :: xs) (y :: ys)) =
length (x :: x' :: xs) * length (y :: ys) | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ length (prod [x] (y :: ys) ++ prod (x' :: xs) (y :: ys)) = length (x :: x' :: xs) * length (y :: ys) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | rw [List.length_append, ih₁, ih₂] | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ length (prod [x] (y :: ys) ++ prod (x' :: xs) (y :: ys)) = length (x :: x' :: xs) * length (y :: ys) | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ length [x] * length (y :: ys) + length (x' :: xs) * length (y :: ys) = length (x :: x' :: xs) * length (y :: ys) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | simp only [length] | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ length [x] * length (y :: ys) + length (x' :: xs) * length (y :: ys) = length (x :: x' :: xs) * length (y :: ys) | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ (0 + 1) * (length ys + 1) + (length xs + 1) * (length ys + 1) = (length xs + 1 + 1) * (length ys + 1) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_prod | [324, 1] | [352, 63] | rw [←Nat.add_mul, Nat.zero_add, Nat.add_comm 1] | α : Type u_1
β : Type u_2
x x' : α
xs : List α
y : β
ys : List β
h_term₁ : Nat.succ 0 + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
h_term₂ : Nat.succ (length xs) + Nat.succ (length ys) < Nat.succ (Nat.succ (length xs)) + Nat.succ (length ys)
ih₁ : length (prod [x] (y :: ys)) = length [x] * length (y :: ys)
ih₂ : length (prod (x' :: xs) (y :: ys)) = length (x' :: xs) * length (y :: ys)
⊢ (0 + 1) * (length ys + 1) + (length xs + 1) * (length ys + 1) = (length xs + 1 + 1) * (length ys + 1) | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_drop | [354, 1] | [361, 14] | simp only [drop, Nat.sub_zero] | α : Type u_1
x✝¹ : List α
x✝ : 0 < length x✝¹
⊢ length (drop 0 x✝¹) = length x✝¹ - 0 | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_drop | [354, 1] | [361, 14] | simp only [drop, Nat.add, length] | α : Type u_1
n : Nat
x : α
xs : List α
h : n + 1 < length (x :: xs)
ih : length (drop n xs) = length xs - n
⊢ length (drop (n + 1) (x :: xs)) = length (x :: xs) - (n + 1) | α : Type u_1
n : Nat
x : α
xs : List α
h : n + 1 < length (x :: xs)
ih : length (drop n xs) = length xs - n
⊢ length (drop n xs) = length xs + 1 - (n + 1) |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_drop | [354, 1] | [361, 14] | rw [Nat.succ_sub_succ_eq_sub] | α : Type u_1
n : Nat
x : α
xs : List α
h : n + 1 < length (x :: xs)
ih : length (drop n xs) = length xs - n
⊢ length (drop n xs) = length xs + 1 - (n + 1) | α : Type u_1
n : Nat
x : α
xs : List α
h : n + 1 < length (x :: xs)
ih : length (drop n xs) = length xs - n
⊢ length (drop n xs) = length xs - n |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_drop | [354, 1] | [361, 14] | exact ih | α : Type u_1
n : Nat
x : α
xs : List α
h : n + 1 < length (x :: xs)
ih : length (drop n xs) = length xs - n
⊢ length (drop n xs) = length xs - n | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_take | [363, 1] | [372, 32] | cases h | α : Type u_1
x✝ : Nat
h : x✝ < length []
⊢ length (take x✝ []) = x✝ | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_take | [363, 1] | [372, 32] | simp only [take, length] | α : Type u_1
x✝¹ : List α
x✝ : 0 < length x✝¹
⊢ length (take 0 x✝¹) = 0 | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_take | [363, 1] | [372, 32] | simp only [take, length] | α : Type u_1
n : Nat
x : α
xs : List α
h : Nat.succ n < length (x :: xs)
ih : length (take n xs) = n
⊢ length (take (Nat.succ n) (x :: xs)) = Nat.succ n | α : Type u_1
n : Nat
x : α
xs : List α
h : Nat.succ n < length (x :: xs)
ih : length (take n xs) = n
⊢ length (take n xs) + 1 = Nat.succ n |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.length_take | [363, 1] | [372, 32] | apply congrArg Nat.succ ih | α : Type u_1
n : Nat
x : α
xs : List α
h : Nat.succ n < length (x :: xs)
ih : length (take n xs) = n
⊢ length (take n xs) + 1 = Nat.succ n | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_eq_filterSpec | [467, 1] | [474, 42] | induction xs with
| nil => simp [filter, filterSpec]
| cons x xs ih =>
simp only [filter, filterSpec]
cases p x with
| true => simp only [ite_true, ih]
| false => simp only [ite_false, ih] | α✝ : Type u_1
p : α✝ → Bool
xs : List α✝
⊢ filter p xs = filterSpec p xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_eq_filterSpec | [467, 1] | [474, 42] | simp [filter, filterSpec] | case nil
α✝ : Type u_1
p : α✝ → Bool
⊢ filter p [] = filterSpec p [] | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_eq_filterSpec | [467, 1] | [474, 42] | simp only [filter, filterSpec] | case cons
α✝ : Type u_1
p : α✝ → Bool
x : α✝
xs : List α✝
ih : filter p xs = filterSpec p xs
⊢ filter p (x :: xs) = filterSpec p (x :: xs) | case cons
α✝ : Type u_1
p : α✝ → Bool
x : α✝
xs : List α✝
ih : filter p xs = filterSpec p xs
⊢ (match p x with
| true => x :: filter p xs
| false => filter p xs) =
if p x = true then x :: filterSpec p xs else filterSpec p xs |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_eq_filterSpec | [467, 1] | [474, 42] | cases p x with
| true => simp only [ite_true, ih]
| false => simp only [ite_false, ih] | case cons
α✝ : Type u_1
p : α✝ → Bool
x : α✝
xs : List α✝
ih : filter p xs = filterSpec p xs
⊢ (match p x with
| true => x :: filter p xs
| false => filter p xs) =
if p x = true then x :: filterSpec p xs else filterSpec p xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_eq_filterSpec | [467, 1] | [474, 42] | simp only [ite_true, ih] | case cons.true
α✝ : Type u_1
p : α✝ → Bool
x : α✝
xs : List α✝
ih : filter p xs = filterSpec p xs
⊢ (match true with
| true => x :: filter p xs
| false => filter p xs) =
if true = true then x :: filterSpec p xs else filterSpec p xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.filter_eq_filterSpec | [467, 1] | [474, 42] | simp only [ite_false, ih] | case cons.false
α✝ : Type u_1
p : α✝ → Bool
x : α✝
xs : List α✝
ih : filter p xs = filterSpec p xs
⊢ (match false with
| true => x :: filter p xs
| false => filter p xs) =
if false = true then x :: filterSpec p xs else filterSpec p xs | no goals |
https://github.com/jrr6/lean-tables.git | 7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712 | Table/BuiltinExtensions.lean | List.reverseAux_spec | [476, 1] | [483, 41] | induction xs generalizing acc with
| nil => simp [reverse, reverseAux]
| cons x xs ih =>
simp only [reverse, reverseAux]
simp only [ih]
rw [←singleton_append, append_assoc] | α : Type u_1
xs acc : List α
⊢ reverseAux xs acc = reverse xs ++ acc | no goals |
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