refactor: Lint
This commit is contained in:
jstoobysmith
parent
a329661c24
commit
e5c85ac109
11 changed files with 179 additions and 182 deletions
|
|
@ -261,7 +261,7 @@ lemma koszulSign_eraseIdx_insertionSortMinPos [IsTotal 𝓕 le] [IsTrans 𝓕 le
|
|||
rfl
|
||||
|
||||
lemma koszulSign_swap_eq_rel_cons {ψ φ : 𝓕}
|
||||
(h1 : le φ ψ) (h2 : le ψ φ) (φs' : List 𝓕):
|
||||
(h1 : le φ ψ) (h2 : le ψ φ) (φs' : List 𝓕) :
|
||||
koszulSign q le (φ :: ψ :: φs') = koszulSign q le (ψ :: φ :: φs') := by
|
||||
simp only [Wick.koszulSign, ← mul_assoc, mul_eq_mul_right_iff]
|
||||
left
|
||||
|
|
@ -285,7 +285,7 @@ lemma koszulSign_eq_rel_eq_stat_append {ψ φ : 𝓕} [IsTrans 𝓕 le] [IsTotal
|
|||
koszulSign q le (φ :: ψ :: φs) = koszulSign q le φs := by
|
||||
intro φs
|
||||
simp [koszulSign, ← mul_assoc]
|
||||
trans 1 * koszulSign q le φs
|
||||
trans 1 * koszulSign q le φs
|
||||
swap
|
||||
simp
|
||||
congr
|
||||
|
|
@ -305,11 +305,11 @@ lemma koszulSign_eq_rel_eq_stat {ψ φ : 𝓕} [IsTrans 𝓕 le] [IsTotal 𝓕 l
|
|||
rw [koszulSign_eq_rel_eq_stat h1 h2 hq φs' φs]
|
||||
simp
|
||||
left
|
||||
trans koszulSignInsert q le φ'' (φ :: ψ :: (φs' ++ φs) )
|
||||
trans koszulSignInsert q le φ'' (φ :: ψ :: (φs' ++ φs))
|
||||
apply koszulSignInsert_eq_perm
|
||||
refine List.Perm.symm (List.perm_cons_append_cons φ ?_)
|
||||
exact List.Perm.symm List.perm_middle
|
||||
rw [koszulSignInsert_eq_remove_same_stat_append q le ]
|
||||
rw [koszulSignInsert_eq_remove_same_stat_append q le]
|
||||
simp_all
|
||||
simp_all
|
||||
simp_all
|
||||
|
|
@ -331,15 +331,16 @@ lemma koszulSign_of_insertionSort [IsTotal 𝓕 le] [IsTrans 𝓕 le] (φs : Lis
|
|||
apply koszulSign_of_sorted
|
||||
exact List.sorted_insertionSort le φs
|
||||
|
||||
lemma koszulSign_of_append_eq_insertionSort_left [IsTotal 𝓕 le] [IsTrans 𝓕 le] : (φs φs' : List 𝓕) →
|
||||
koszulSign q le (φs ++ φs') =
|
||||
koszulSign q le (List.insertionSort le φs ++ φs') * koszulSign q le φs
|
||||
lemma koszulSign_of_append_eq_insertionSort_left [IsTotal 𝓕 le] [IsTrans 𝓕 le] :
|
||||
(φs φs' : List 𝓕) → koszulSign q le (φs ++ φs') =
|
||||
koszulSign q le (List.insertionSort le φs ++ φs') * koszulSign q le φs
|
||||
| φs, [] => by
|
||||
simp
|
||||
| φs, φ :: φs' => by
|
||||
have h1 : (φs ++ φ :: φs') = List.insertIdx φs.length φ (φs ++ φs') := by
|
||||
rw [insertIdx_length_fst_append]
|
||||
have h2 : (List.insertionSort le φs ++ φ :: φs') = List.insertIdx (List.insertionSort le φs).length φ (List.insertionSort le φs ++ φs') := by
|
||||
have h2 : (List.insertionSort le φs ++ φ :: φs') =
|
||||
List.insertIdx (List.insertionSort le φs).length φ (List.insertionSort le φs ++ φs') := by
|
||||
rw [insertIdx_length_fst_append]
|
||||
rw [h1, h2]
|
||||
rw [koszulSign_insertIdx]
|
||||
|
|
@ -353,7 +354,8 @@ lemma koszulSign_of_append_eq_insertionSort_left [IsTotal 𝓕 le] [IsTrans 𝓕
|
|||
simp [mul_comm]
|
||||
left
|
||||
congr 3
|
||||
· have h2 : (List.insertionSort le φs ++ φ :: φs') = List.insertIdx φs.length φ (List.insertionSort le φs ++ φs') := by
|
||||
· have h2 : (List.insertionSort le φs ++ φ :: φs') =
|
||||
List.insertIdx φs.length φ (List.insertionSort le φs ++ φs') := by
|
||||
rw [← insertIdx_length_fst_append]
|
||||
simp
|
||||
rw [insertionSortEquiv_congr _ _ h2.symm]
|
||||
|
|
@ -363,16 +365,16 @@ lemma koszulSign_of_append_eq_insertionSort_left [IsTotal 𝓕 le] [IsTrans 𝓕
|
|||
rw [insertionSortEquiv_congr _ _ h1.symm]
|
||||
simp
|
||||
· rw [insertIdx_length_fst_append]
|
||||
rw [show φs.length = (List.insertionSort le φs).length by simp]
|
||||
rw [show φs.length = (List.insertionSort le φs).length by simp]
|
||||
rw [insertIdx_length_fst_append]
|
||||
symm
|
||||
apply insertionSort_insertionSort_append
|
||||
· simp
|
||||
· simp
|
||||
|
||||
lemma koszulSign_of_append_eq_insertionSort [IsTotal 𝓕 le] [IsTrans 𝓕 le] : (φs'' φs φs' : List 𝓕) →
|
||||
lemma koszulSign_of_append_eq_insertionSort [IsTotal 𝓕 le] [IsTrans 𝓕 le] : (φs'' φs φs' : List 𝓕) →
|
||||
koszulSign q le (φs'' ++ φs ++ φs') =
|
||||
koszulSign q le (φs'' ++ List.insertionSort le φs ++ φs') * koszulSign q le φs
|
||||
koszulSign q le (φs'' ++ List.insertionSort le φs ++ φs') * koszulSign q le φs
|
||||
| [], φs, φs'=> by
|
||||
simp
|
||||
exact koszulSign_of_append_eq_insertionSort_left q le φs φs'
|
||||
|
|
@ -391,10 +393,10 @@ lemma koszulSign_of_append_eq_insertionSort [IsTotal 𝓕 le] [IsTrans 𝓕 le]
|
|||
|
||||
-/
|
||||
|
||||
lemma koszulSign_perm_eq_append [IsTotal 𝓕 le] [IsTrans 𝓕 le] (φ : 𝓕) ( φs φs' φs2 : List 𝓕)
|
||||
lemma koszulSign_perm_eq_append [IsTotal 𝓕 le] [IsTrans 𝓕 le] (φ : 𝓕) (φs φs' φs2 : List 𝓕)
|
||||
(hp : φs.Perm φs') : (h : ∀ φ' ∈ φs, le φ φ' ∧ le φ' φ) →
|
||||
koszulSign q le (φs ++ φs2) = koszulSign q le (φs' ++ φs2) := by
|
||||
let motive (φs φs' : List 𝓕) (hp : φs.Perm φs') : Prop :=
|
||||
let motive (φs φs' : List 𝓕) (hp : φs.Perm φs') : Prop :=
|
||||
(h : ∀ φ' ∈ φs, le φ φ' ∧ le φ' φ) →
|
||||
koszulSign q le (φs ++ φs2) = koszulSign q le (φs' ++ φs2)
|
||||
change motive φs φs' hp
|
||||
|
|
@ -433,5 +435,4 @@ lemma koszulSign_perm_eq [IsTotal 𝓕 le] [IsTrans 𝓕 le] (φ : 𝓕) : (φs1
|
|||
refine (List.perm_append_right_iff φs2).mpr ?_
|
||||
exact List.Perm.append_left φs1 hp
|
||||
|
||||
|
||||
end Wick
|
||||
|
|
|
|||
|
|
@ -235,7 +235,7 @@ lemma koszulSignInsert_cons (r0 r1 : 𝓕) (r : List 𝓕) :
|
|||
koszulSignInsert q le r0 r := by
|
||||
simp [koszulSignInsert, koszulSignCons]
|
||||
|
||||
lemma koszulSignInsert_of_le_mem (φ0 : 𝓕) : (φs : List 𝓕) → (h : ∀ b ∈ φs, le φ0 b) →
|
||||
lemma koszulSignInsert_of_le_mem (φ0 : 𝓕) : (φs : List 𝓕) → (h : ∀ b ∈ φs, le φ0 b) →
|
||||
koszulSignInsert q le φ0 φs = 1
|
||||
| [], _ => by
|
||||
simp [koszulSignInsert]
|
||||
|
|
@ -247,7 +247,6 @@ lemma koszulSignInsert_of_le_mem (φ0 : 𝓕) : (φs : List 𝓕) → (h : ∀
|
|||
exact h b (List.mem_cons_of_mem _ hb)
|
||||
· exact h φ1 (List.mem_cons_self _ _)
|
||||
|
||||
|
||||
lemma koszulSignInsert_eq_rel_eq_stat {ψ φ : 𝓕} [IsTotal 𝓕 le] [IsTrans 𝓕 le]
|
||||
(h1 : le φ ψ) (h2 : le ψ φ) (hq : q ψ = q φ) : (φs : List 𝓕) →
|
||||
koszulSignInsert q le φ φs = koszulSignInsert q le ψ φs
|
||||
|
|
@ -270,7 +269,7 @@ lemma koszulSignInsert_eq_rel_eq_stat {ψ φ : 𝓕} [IsTotal 𝓕 le] [IsTrans
|
|||
rw [koszulSignInsert_eq_rel_eq_stat h1 h2 hq φs]
|
||||
|
||||
lemma koszulSignInsert_eq_remove_same_stat_append {ψ φ φ' : 𝓕} [IsTotal 𝓕 le] [IsTrans 𝓕 le]
|
||||
(h1 : le φ ψ) (h2 : le ψ φ) (hq : q ψ = q φ) : ( φs : List 𝓕) →
|
||||
(h1 : le φ ψ) (h2 : le ψ φ) (hq : q ψ = q φ) : (φs : List 𝓕) →
|
||||
koszulSignInsert q le φ' (φ :: ψ :: φs) = koszulSignInsert q le φ' φs := by
|
||||
intro φs
|
||||
simp_all [koszulSignInsert]
|
||||
|
|
@ -284,6 +283,4 @@ lemma koszulSignInsert_eq_remove_same_stat_append {ψ φ φ' : 𝓕} [IsTotal
|
|||
apply IsTrans.trans φ' ψ φ hφ'ψ h2
|
||||
simp_all [hφ'φ, hφ'ψ]
|
||||
|
||||
|
||||
|
||||
end Wick
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue