refactor: Replace simp proofs

HepLean/SpaceTime/LorentzVector/Contraction.lean

@@ -56,8 +56,7 @@ def contrUpDownBi : LorentzVector d →ₗ[ℝ] CovariantLorentzVector d →ₗ[
     rw [Finset.smul_sum]
     refine Finset.sum_congr rfl (fun i _ => ?_)
     simp only [HSMul.hSMul, SMul.smul]
-    simp only [RingHom.id, RingHom.coe_mk, MonoidHom.coe_mk, OneHom.coe_mk, id_eq]
-    ring
+    exact mul_assoc r (v i) (w i)
 
 /-- The linear map defining the contraction of a contravariant Lorentz vector
   and a covariant Lorentz vector. -/
@@ -185,9 +184,10 @@ lemma asTenProd_diag :
   rw [Finset.sum_eq_single μ]
   · intro ν _ hμν
     rw [minkowskiMatrix.off_diag_zero hμν.symm]
-    simp only [zero_smul]
+    exact TensorProduct.zero_smul (e μ ⊗ₜ[ℝ] e ν)
   · intro a
-    simp_all only
+    rename_i j
+    exact False.elim (a j)
 
 /-- The metric tensor as an element of `CovariantLorentzVector d ⊗[ℝ] CovariantLorentzVector d`. -/
 def asCoTenProd : CovariantLorentzVector d ⊗[ℝ] CovariantLorentzVector d :=

HepLean/SpaceTime/LorentzVector/Covariant.lean

@@ -101,7 +101,7 @@ lemma rep_apply_stdBasis (g : LorentzGroup d) (μ : Fin 1 ⊕ Fin d) :
   simp [LorentzVector.stdBasis, Pi.basisFun_apply]
   erw [Pi.basisFun_apply, Matrix.mulVec_stdBasis]
   rw [← LorentzGroup.coe_inv]
-  simp
+  rfl
 
 end CovariantLorentzVector
 

HepLean/SpaceTime/LorentzVector/LorentzAction.lean

@@ -20,8 +20,7 @@ variable {d : ℕ} (v : LorentzVector d)
 /-- The contravariant action of the Lorentz group on a Lorentz vector. -/
 def rep : Representation ℝ (LorentzGroup d) (LorentzVector d) where
   toFun g := Matrix.toLinAlgEquiv e g
-  map_one' := by
-    simp only [lorentzGroupIsGroup_one_coe, map_one]
+  map_one' := (MulEquivClass.map_eq_one_iff (Matrix.toLinAlgEquiv e)).mpr rfl
   map_mul' x y := by
     simp only [lorentzGroupIsGroup_mul_coe, map_mul]