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refactor: Lint

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jstoobysmith 2024-12-19 15:40:04 +00:00
parent c993de36f6
commit cd63ec0716
13 changed files with 181 additions and 84 deletions
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34
HepLean/PerturbationTheory/Wick/Signs/KoszulSign.lean
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@ -24,7 +24,6 @@ def koszulSign {I : Type} (r : I → I → Prop) [DecidableRel r] (q : I → Fin
| [] => 1
| a :: l => koszulSignInsert r q a l * koszulSign r q l
lemma koszulSign_mul_self {I : Type} (r : I → I → Prop) [DecidableRel r] (q : I → Fin 2)
(l : List I) : koszulSign r q l * koszulSign r q l = 1 := by
induction l with
@ -84,36 +83,6 @@ lemma koszulSign_erase_boson {I : Type} (q : I → Fin 2) (le1 :I → I → Prop
rw [koszulSignInsert_erase_boson q le1 r0 r ⟨n, Nat.succ_lt_succ_iff.mp h⟩ h']
exact h'
def koszulSignCons {I : Type} (q : I → Fin 2) (le1 : I → I → Prop) [DecidableRel le1] (r0 r1 : I) :
ℂ :=
if le1 r0 r1 then 1 else
if q r0 = 1 ∧ q r1 = 1 then -1 else 1
lemma koszulSignCons_eq_superComuteCoef {I : Type} (q : I → Fin 2) (le1 : I → I → Prop)
[DecidableRel le1] (r0 r1 : I) : koszulSignCons q le1 r0 r1 =
if le1 r0 r1 then 1 else superCommuteCoef q [r0] [r1] := by
simp only [koszulSignCons, Fin.isValue, superCommuteCoef, grade, ite_eq_right_iff, zero_ne_one,
imp_false]
congr 1
by_cases h0 : q r0 = 1
· by_cases h1 : q r1 = 1
· simp [h0, h1]
· have h1 : q r1 = 0 := by omega
simp [h0, h1]
· have h0 : q r0 = 0 := by omega
by_cases h1 : q r1 = 1
· simp [h0, h1]
· have h1 : q r1 = 0 := by omega
simp [h0, h1]
lemma koszulSignInsert_cons {I : Type} (q : I → Fin 2) (le1 : I → I → Prop) [DecidableRel le1]
[IsTotal I le1] [IsTrans I le1] (r0 r1 : I) (r : List I) :
koszulSignInsert le1 q r0 (r1 :: r) = (koszulSignCons q le1 r0 r1) *
koszulSignInsert le1 q r0 r := by
simp [koszulSignInsert, koszulSignCons]
lemma koszulSign_insertIdx {I : Type} (q : I → Fin 2) (le1 : I → I → Prop) [DecidableRel le1]
(i : I) [IsTotal I le1] [IsTrans I le1] : (r : List I) → (n : ℕ) → (hn : n ≤ r.length) →
koszulSign le1 q (List.insertIdx n i r) = insertSign q n i r
@ -199,8 +168,6 @@ lemma koszulSign_insertIdx {I : Type} (q : I → Fin 2) (le1 : I → I → Prop)
rw [← insertionSortEquiv_get]
simp only [Function.comp_apply, Equiv.symm_apply_apply, List.get_eq_getElem, ni]
simp_all only [List.length_cons, add_le_add_iff_right, List.getElem_insertIdx_self]
have hms : (List.orderedInsert le1 r0 rs).get ⟨nro, by simp⟩ = r0 := by
simp [nro]
have hc1 : ni.castSucc < nro → ¬ le1 r0 i := by
intro hninro
rw [← hns]
@ -231,5 +198,4 @@ lemma koszulSign_insertIdx {I : Type} (q : I → Fin 2) (le1 : I → I → Prop)
· exact Nat.le_of_lt_succ h
· exact Nat.le_of_lt_succ h
end Wick