feat: Some simple extensions of lemmas

HepLean/Tensors/Tree/NodeIdentities/Basic.lean

@@ -140,7 +140,7 @@ lemma perm_eq_iff_eq_perm {n m : ℕ} {c : Fin n → S.C} {c1 : Fin m → S.C}
       apply Hom.ext
       ext x
       change (Hom.toEquiv σ) ((Hom.toEquiv σ).symm x) = x
-      simp
+      simp [-OverColor.mk_left]
     rw [h1]
     simp
 

HepLean/Tensors/Tree/NodeIdentities/PermProd.lean

@@ -35,6 +35,11 @@ def permProdLeft := (equivToIso finSumFinEquiv).inv ≫ σ ▷ OverColor.mk c2
 def permProdRight := (equivToIso finSumFinEquiv).inv ≫ OverColor.mk c2 ◁ σ
   ≫ (equivToIso finSumFinEquiv).hom
 
+@[simp]
+lemma permProdRight_toEquiv : Hom.toEquiv (permProdRight c2 σ) =  finSumFinEquiv.symm.trans
+    (((Equiv.refl (Fin n2)).sumCongr (Hom.toEquiv σ)).trans finSumFinEquiv)  := by
+  simp [permProdRight]
+
 /-- When a `prod` acts on a `perm` node in the left entry, the `perm` node can be moved through
   the `prod` node via right-whiskering. -/
 theorem prod_perm_left (t : TensorTree S c) (t2 : TensorTree S c2) :

HepLean/Tensors/Tree/NodeIdentities/ProdComm.lean

@@ -31,6 +31,11 @@ def braidPerm : OverColor.mk (Sum.elim c2 c ∘ ⇑finSumFinEquiv.symm) ⟶
   (β_ (OverColor.mk c2) (OverColor.mk c)).hom
   ≫ (equivToIso finSumFinEquiv).hom
 
+@[simp]
+lemma braidPerm_toEquiv : Hom.toEquiv (braidPerm c c2) = finSumFinEquiv.symm.trans
+    ((Equiv.sumComm (Fin n2) (Fin n)).trans finSumFinEquiv) := by
+  simp [braidPerm]
+
 lemma finSumFinEquiv_comp_braidPerm :
     (equivToIso finSumFinEquiv).hom ≫ braidPerm c c2 =
     (β_ (OverColor.mk c2) (OverColor.mk c)).hom