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refactor: replace some simp with exact

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jstoobysmith 2024-08-30 10:43:29 -04:00
parent 167145acef
commit 81f3566be8
13 changed files with 82 additions and 102 deletions
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24
HepLean/AnomalyCancellation/PureU1/Odd/LineInCubic.lean
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@ -73,15 +73,8 @@ lemma lineInCubicPerm_self {S : (PureU1 (2 * n + 1)).LinSols} (hS : LineInCubicP
/-- If `lineInCubicPerm S`, then `lineInCubicPerm (M S)` for all permutations `M`. -/
lemma lineInCubicPerm_permute {S : (PureU1 (2 * n + 1)).LinSols}
(hS : LineInCubicPerm S) (M' : (FamilyPermutations (2 * n + 1)).group) :
LineInCubicPerm ((FamilyPermutations (2 * n + 1)).linSolRep M' S) := by
rw [LineInCubicPerm]
intro M
have ht : ((FamilyPermutations (2 * n + 1)).linSolRep M)
((FamilyPermutations (2 * n + 1)).linSolRep M' S)
= (FamilyPermutations (2 * n + 1)).linSolRep (M * M') S := by
simp [(FamilyPermutations (2 * n.succ)).linSolRep.map_mul']
rw [ht]
exact hS (M * M')
LineInCubicPerm ((FamilyPermutations (2 * n + 1)).linSolRep M' S) :=
fun M => hS (M * M')
lemma lineInCubicPerm_swap {S : (PureU1 (2 * n.succ + 1)).LinSols}
(LIC : LineInCubicPerm S) :
@ -108,10 +101,7 @@ lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
rw [P_P_P!_accCube f 0]
rw [← Pa_δa₁ f g]
rw [← hS]
have ht : δ!₁ (0 : Fin n.succ.succ) = δ₁ 1 := by
simp [δ!₁, δ₁]
rw [Fin.ext_iff]
simp
have ht : δ!₁ (0 : Fin n.succ.succ) = δ₁ 1 := rfl
nth_rewrite 1 [ht]
rw [P_δ₁]
have h1 := Pa_δa₁ f g
@ -125,7 +115,7 @@ lemma P_P_P!_accCube' {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
rw [δa₄_δ!₂]
have h0 : (δa₂ (0 : Fin n.succ)) = δ!₁ 0 := by
rw [δa₂_δ!₁]
simp
exact ht
rw [h0, δa₁_δ!₃]
ring
@ -149,9 +139,9 @@ lemma lineInCubicPerm_last_perm {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}
(LIC : LineInCubicPerm S) : LineInPlaneCond S := by
refine @Prop_three (2 * n.succ.succ + 1) LineInPlaneProp S (δ!₂ 0) (δ!₁ 0)
δ!₃ ?_ ?_ ?_ ?_
· simp [Fin.ext_iff, δ!₂, δ!₁]
· simp [Fin.ext_iff, δ!₂, δ!₃]
· simp [Fin.ext_iff, δ!₁, δ!₃]
· exact ne_of_beq_false rfl
· exact ne_of_beq_false rfl
· exact ne_of_beq_false rfl
· exact fun M => lineInCubicPerm_last_cond (lineInCubicPerm_permute LIC M)
lemma lineInCubicPerm_constAbs {S : (PureU1 (2 * n.succ.succ + 1)).LinSols}