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refactor: simp with simp only

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jstoobysmith 2024-10-16 11:09:52 +00:00
parent a1d3616a18
commit aea1e88561
4 changed files with 137 additions and 44 deletions
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23
HepLean/SpaceTime/LorentzVector/AsSelfAdjointMatrix.lean
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@ -38,7 +38,8 @@ lemma toSelfAdjointMatrix_apply (x : LorentzVector 3) : toSelfAdjointMatrix x =
Basis.coe_mk, Fin.isValue]
rw [Finsupp.linearCombination_apply_of_mem_supported ℝ (s := Finset.univ)]
· change (∑ i : Fin 1 ⊕ Fin 3, x i • PauliMatrix.σSAL' i) = _
simp [Fin.sum_univ_three, PauliMatrix.σSAL']
simp only [PauliMatrix.σSAL', Fintype.sum_sum_type, Finset.univ_unique, Fin.default_eq_zero,
Fin.isValue, Finset.sum_singleton, Fin.sum_univ_three]
apply Subtype.ext
simp only [Fin.isValue, AddSubgroup.coe_add, selfAdjoint.val_smul, smul_neg,
AddSubgroupClass.coe_sub]
@ -58,23 +59,29 @@ lemma toSelfAdjointMatrix_stdBasis (i : Fin 1 ⊕ Fin 3) :
rw [toSelfAdjointMatrix_apply]
match i with
| Sum.inl 0 =>
simp [LorentzVector.stdBasis]
simp only [LorentzVector.stdBasis, Fin.isValue]
erw [Pi.basisFun_apply]
simp [PauliMatrix.σSAL, PauliMatrix.σSAL']
| Sum.inr 0 =>
simp [LorentzVector.stdBasis]
simp only [LorentzVector.stdBasis, Fin.isValue]
erw [Pi.basisFun_apply]
simp [PauliMatrix.σSAL, PauliMatrix.σSAL']
simp only [Fin.isValue, ne_eq, reduceCtorEq, not_false_eq_true, Pi.single_eq_of_ne, zero_smul,
Pi.single_eq_same, one_smul, zero_sub, Sum.inr.injEq, one_ne_zero, sub_zero, Fin.reduceEq,
PauliMatrix.σSAL, Basis.coe_mk, PauliMatrix.σSAL']
refine Eq.symm (PauliMatrix.selfAdjoint_ext rfl rfl rfl rfl)
| Sum.inr 1 =>
simp [LorentzVector.stdBasis]
simp only [LorentzVector.stdBasis, Fin.isValue]
erw [Pi.basisFun_apply]
simp [PauliMatrix.σSAL, PauliMatrix.σSAL']
simp only [Fin.isValue, ne_eq, reduceCtorEq, not_false_eq_true, Pi.single_eq_of_ne, zero_smul,
Sum.inr.injEq, zero_ne_one, sub_self, Pi.single_eq_same, one_smul, zero_sub, Fin.reduceEq,
sub_zero, PauliMatrix.σSAL, Basis.coe_mk, PauliMatrix.σSAL']
refine Eq.symm (PauliMatrix.selfAdjoint_ext rfl rfl rfl rfl)
| Sum.inr 2 =>
simp [LorentzVector.stdBasis]
simp only [LorentzVector.stdBasis, Fin.isValue]
erw [Pi.basisFun_apply]
simp [PauliMatrix.σSAL, PauliMatrix.σSAL']
simp only [Fin.isValue, ne_eq, reduceCtorEq, not_false_eq_true, Pi.single_eq_of_ne, zero_smul,
Sum.inr.injEq, Fin.reduceEq, sub_self, Pi.single_eq_same, one_smul, zero_sub,
PauliMatrix.σSAL, Basis.coe_mk, PauliMatrix.σSAL']
refine Eq.symm (PauliMatrix.selfAdjoint_ext rfl rfl rfl rfl)
@[simp]