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refactor: simp golfing

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This commit is contained in:
jstoobysmith 2024-08-30 10:11:55 -04:00
parent d39c6c3e28
commit 167145acef
8 changed files with 35 additions and 75 deletions
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22
HepLean/AnomalyCancellation/PureU1/Even/BasisLinear.lean
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@ -566,9 +566,10 @@ theorem basis_linear_independent : LinearIndependent ℚ (@basis n) := by
apply Fintype.linearIndependent_iff.mpr
intro f h
change P' f = 0 at h
have h1 : (P' f).val = 0 := by
simp [h]
rfl
have h1 : (P' f).val = 0 :=
(AddSemiconjBy.eq_zero_iff (ACCSystemLinear.LinSols.val 0)
(congrFun (congrArg HAdd.hAdd (congrArg ACCSystemLinear.LinSols.val (id (Eq.symm h))))
(ACCSystemLinear.LinSols.val 0))).mp rfl
rw [P'_val] at h1
exact P_zero f h1
@ -576,9 +577,10 @@ theorem basis!_linear_independent : LinearIndependent ℚ (@basis! n) := by
apply Fintype.linearIndependent_iff.mpr
intro f h
change P!' f = 0 at h
have h1 : (P!' f).val = 0 := by
simp [h]
rfl
have h1 : (P!' f).val = 0 :=
(AddSemiconjBy.eq_zero_iff (ACCSystemLinear.LinSols.val 0)
(congrFun (congrArg HAdd.hAdd (congrArg ACCSystemLinear.LinSols.val (id (Eq.symm h))))
(ACCSystemLinear.LinSols.val 0))).mp rfl
rw [P!'_val] at h1
exact P!_zero f h1
@ -586,9 +588,10 @@ theorem basisa_linear_independent : LinearIndependent ℚ (@basisa n) := by
apply Fintype.linearIndependent_iff.mpr
intro f h
change Pa' f = 0 at h
have h1 : (Pa' f).val = 0 := by
simp [h]
rfl
have h1 : (Pa' f).val = 0 :=
(AddSemiconjBy.eq_zero_iff (ACCSystemLinear.LinSols.val 0)
(congrFun (congrArg HAdd.hAdd (congrArg ACCSystemLinear.LinSols.val (id (Eq.symm h))))
(ACCSystemLinear.LinSols.val 0))).mp rfl
rw [Pa'_P'_P!'] at h1
change (P' (f ∘ Sum.inl)).val + (P!' (f ∘ Sum.inr)).val = 0 at h1
rw [P!'_val, P'_val] at h1
@ -728,7 +731,6 @@ lemma vectorLikeEven_in_span (S : (PureU1 (2 * n.succ)).LinSols)
rw [ht]
ring
rw [h]
simp
rfl
end VectorLikeEvenPlane