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refactor: lint

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jstoobysmith 2025-02-03 11:42:56 +00:00
parent 6433259bc4
commit 70f617096b
16 changed files with 103 additions and 87 deletions
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25
HepLean/PerturbationTheory/WickContraction/Sign/Join.lean
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@ -205,10 +205,8 @@ lemma join_singleton_sign_right {φs : List 𝓕.FieldOp}
rw [sign_right_eq_prod_mul_prod]
rfl
lemma joinSignRightExtra_eq_i_j_finset_eq_if {φs : List 𝓕.FieldOp}
{i j : Fin φs.length} (h : i < j)
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
{i j : Fin φs.length} (h : i < j) (φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
joinSignRightExtra h φsucΛ = ∏ a,
𝓢((𝓕|>ₛ [singleton h]ᵘᶜ[φsucΛ.sndFieldOfContract a]),
𝓕 |>ₛ ⟨φs.get, (if uncontractedListEmd (φsucΛ.fstFieldOfContract a) < j ∧
@ -303,13 +301,10 @@ lemma joinSignLeftExtra_eq_joinSignRightExtra {φs : List 𝓕.FieldOp}
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
joinSignLeftExtra h φsucΛ = joinSignRightExtra h φsucΛ := by
/- Simplifying joinSignLeftExtra. -/
rw [joinSignLeftExtra]
rw [ofFinset_eq_prod]
rw [map_prod]
let e2 : Fin φs.length ≃ {x // (((singleton h).join φsucΛ).getDual? x).isSome} ⊕
{x // ¬ (((singleton h).join φsucΛ).getDual? x).isSome} := by
exact (Equiv.sumCompl fun a => (((singleton h).join φsucΛ).getDual? a).isSome = true).symm
rw [← e2.symm.prod_comp]
rw [joinSignLeftExtra, ofFinset_eq_prod, map_prod, ← e2.symm.prod_comp]
simp only [Fin.getElem_fin, Fintype.prod_sum_type, instCommGroup]
conv_lhs =>
enter [2, 2, x]
@ -326,8 +321,7 @@ lemma joinSignLeftExtra_eq_joinSignRightExtra {φs : List 𝓕.FieldOp}
enter [2, a]
rw [prod_finset_eq_mul_fst_snd]
simp [e2, sigmaContractedEquiv]
rw [prod_join]
rw [singleton_prod]
rw [prod_join, singleton_prod]
simp only [join_fstFieldOfContract_joinLiftLeft, singleton_fstFieldOfContract,
join_sndFieldOfContract_joinLift, singleton_sndFieldOfContract, lt_self_iff_false, and_false,
↓reduceIte, map_one, mul_one, join_fstFieldOfContract_joinLiftRight,
@ -384,17 +378,14 @@ lemma join_sign_singleton {φs : List 𝓕.FieldOp}
{i j : Fin φs.length} (h : i < j) (hs : (𝓕 |>ₛ φs[i]) = (𝓕 |>ₛ φs[j]))
(φsucΛ : WickContraction [singleton h]ᵘᶜ.length) :
(join (singleton h) φsucΛ).sign = (singleton h).sign * φsucΛ.sign := by
rw [join_singleton_sign_right]
rw [join_singleton_sign_left h φsucΛ]
rw [join_singleton_sign_right, join_singleton_sign_left h φsucΛ]
rw [joinSignLeftExtra_eq_joinSignRightExtra h hs φsucΛ]
rw [← mul_assoc]
rw [mul_assoc _ _ (joinSignRightExtra h φsucΛ)]
rw [← mul_assoc, mul_assoc _ _ (joinSignRightExtra h φsucΛ)]
have h1 : (joinSignRightExtra h φsucΛ * joinSignRightExtra h φsucΛ) = 1 := by
rw [← joinSignLeftExtra_eq_joinSignRightExtra h hs φsucΛ]
simp [joinSignLeftExtra]
simp only [instCommGroup, Fin.getElem_fin, h1, mul_one]
rw [sign]
rw [prod_join]
rw [sign, prod_join]
congr
· rw [singleton_prod]
simp
@ -414,9 +405,7 @@ lemma join_sign_induction {φs : List 𝓕.FieldOp} (φsΛ : WickContraction φs
| Nat.succ n, hn => by
obtain ⟨i, j, hij, φsucΛ', rfl, h1, h2, h3⟩ :=
exists_join_singleton_of_card_ge_zero φsΛ (by simp [hn]) hc
rw [join_assoc]
rw [join_sign_singleton hij h1]
rw [join_sign_singleton hij h1]
rw [join_assoc, join_sign_singleton hij h1, join_sign_singleton hij h1]
have hn : φsucΛ'.1.card = n := by
omega
rw [join_sign_induction φsucΛ' (congr (by simp [join_uncontractedListGet]) φsucΛ) h2