DibyashanuPati/PhysLean
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refactor: Replace some simp with simp?

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jstoobysmith 2024-09-04 07:31:34 -04:00
parent 03edf78931
commit fccb283a5c
14 changed files with 110 additions and 85 deletions
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16
HepLean/SpaceTime/LorentzTensor/RisingLowering.lean
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@ -58,8 +58,8 @@ def boolFin (c₁ c₂ : 𝓒.ColorMap (Fin n)) : Bool :=
omit [Fintype 𝓒.Color] in
lemma boolFin_DualMap {c₁ c₂ : 𝓒.ColorMap (Fin n)} (h : boolFin c₁ c₂ = true) :
DualMap c₁ c₂ := by
simp [boolFin] at h
simp [DualMap]
simp only [boolFin, Bool.if_false_right, Bool.and_true, List.all_eq_true, decide_eq_true_eq] at h
simp only [DualMap]
funext x
have h2 {n : ℕ} (m : Fin n) : m ∈ Fin.list n := by
have h1' : (Fin.list n)[m] = m := by
@ -76,8 +76,8 @@ def boolFin' (c₁ c₂ : 𝓒.ColorMap (Fin n)) : Bool :=
omit [Fintype 𝓒.Color]
lemma boolFin'_DualMap {c₁ c₂ : 𝓒.ColorMap (Fin n)} (h : boolFin' c₁ c₂ = true) :
DualMap c₁ c₂ := by
simp [boolFin'] at h
simp [DualMap]
simp only [boolFin', decide_eq_true_eq] at h
simp only [DualMap]
funext x
exact h x
@ -103,7 +103,7 @@ lemma dual_eq_of_neq (h : DualMap c₁ c₂) {x : X} (h' : c₁ x ≠ c₂ x) :
𝓒.τ (c₁ x) = c₂ x := by
rw [DualMap] at h
have h1 := congrFun h x
simp [colorQuot, HasEquiv.Equiv, Setoid.r, colorRel] at h1
simp only [Function.comp_apply, colorQuot, Quotient.eq, HasEquiv.Equiv, Setoid.r, colorRel] at h1
simp_all only [ne_eq, false_or]
exact 𝓒.τ_involutive (c₂ x)
@ -270,7 +270,7 @@ def dualizeAll : 𝓣.Tensor cX ≃ₗ[R] 𝓣.Tensor (𝓣.τ ∘ cX) := by
apply LinearMap.ext
refine fun x ↦ PiTensorProduct.induction_on' x ?_ (by
intro a b hx a
simp [map_add, add_tmul, hx]
simp only [Function.comp_apply, map_add, hx, LinearMap.id_coe, id_eq, LinearMap.coe_comp]
simp_all only [Function.comp_apply, LinearMap.coe_comp, LinearMap.id_coe, id_eq])
intro rx fx
simp only [Function.comp_apply, PiTensorProduct.tprodCoeff_eq_smul_tprod,
@ -287,10 +287,10 @@ lemma dualizeAll_equivariant (g : G) : (𝓣.dualizeAll.toLinearMap) ∘ₗ (@re
= 𝓣.rep g ∘ₗ (𝓣.dualizeAll.toLinearMap) := by
apply LinearMap.ext
intro x
simp [dualizeAll]
simp only [dualizeAll, Function.comp_apply, LinearEquiv.ofLinear_toLinearMap, LinearMap.coe_comp]
refine PiTensorProduct.induction_on' x ?_ (by
intro a b hx a
simp [map_add, add_tmul, hx]
simp only [map_add, hx]
simp_all only [Function.comp_apply, LinearMap.coe_comp, LinearMap.id_coe, id_eq])
intro rx fx
simp only [PiTensorProduct.tprodCoeff_eq_smul_tprod, LinearMapClass.map_smul, rep_tprod]