refactor: Index notation, computablity

HepLean/SpaceTime/LorentzTensor/IndexNotation/Relations.lean

@@ -62,6 +62,13 @@ namespace ContrPerm
 
 variable {l l' l2 l3 : ColorIndexList 𝓒}
 
+lemma of_perm (h : l.contr.val.Perm l'.contr.val) : l.ContrPerm l' := by
+  apply And.intro
+  exact List.Perm.length_eq h
+  apply And.intro
+  sorry
+  sorry
+
 @[symm]
 lemma symm (h : ContrPerm l l') : ContrPerm l' l := by
   rw [ContrPerm] at h ⊢
@@ -85,16 +92,16 @@ lemma trans (h1 : ContrPerm l l2) (h2 : ContrPerm l2 l3) : ContrPerm l l3 := by
   funext i
   simp only [Function.comp_apply]
   have h1' := congrFun h1.2.2 ⟨i, by simp [h1.2.1]⟩
-  simp at h1'
+  simp only [Function.comp_apply] at h1'
   rw [← h1']
   have h2' := congrFun h2.2.2 ⟨
     ↑((l.contr.getDualInOtherEquiv l2.contr.toIndexList) ⟨↑i, by simp [h1.2.1]⟩), by simp [h2.2.1]⟩
-  simp at h2'
+  simp only [Function.comp_apply] at h2'
   rw [← h2']
   apply congrArg
   simp only [getDualInOtherEquiv, Equiv.coe_fn_mk]
   rw [← eq_getDualInOther?_get_of_withUniqueDualInOther_iff]
-  simp [AreDualInOther]
+  simp only [AreDualInOther, getDualInOther?_id]
   rw [h2.2.1]
   simp
 
@@ -108,8 +115,8 @@ lemma contr_self : ContrPerm l l.contr := by
   simp only [contr_contr, true_and]
   have h1 := @refl _ _ l
   apply And.intro h1.2.1
-  erw [contr_contr]
-  exact h1.2.2
+  rw [show l.contr.contr = l.contr by simp]
+  simp only [getDualInOtherEquiv_self_refl, Equiv.coe_refl, CompTriple.comp_eq]
 
 @[simp]
 lemma self_contr : ContrPerm l.contr l := by