refactor(library): cleanup

library/algebra/group.lean

@@ -297,7 +297,7 @@ section group
 
   lemma is_conj.symm (a b : A) : a ~ b → b ~ a :=
       assume Pab, obtain x (Pconj : x ∘c b = a), from Pab,
-      assert Pxinv : x⁻¹ ∘c x ∘c b = x⁻¹ ∘c a, from (congr_arg2 conj_by (eq.refl x⁻¹) Pconj),
+      assert Pxinv : x⁻¹ ∘c x ∘c b = x⁻¹ ∘c a,   begin congruence, assumption end,
       exists.intro x⁻¹ (eq.symm (conj_inv_cancel x b ▸ Pxinv))
 
   lemma is_conj.trans (a b c : A) : a ~ b → b ~ c → a ~ c :=

library/init/logic.lean

@@ -347,7 +347,7 @@ iff_true_intro not_false
 theorem not_congr [congr] (H : a ↔ b) : ¬a ↔ ¬b :=
 iff.intro (λ H₁ H₂, H₁ (iff.mpr H H₂)) (λ H₁ H₂, H₁ (iff.mp H H₂))
 
-theorem ne_self_iff_false {A : Type} (a : A) : (a ≠ a) ↔ false :=
+theorem ne_self_iff_false [simp] {A : Type} (a : A) : (not (a = a)) ↔ false :=
 iff.intro false_of_ne false.elim
 
 theorem eq_self_iff_true [simp] {A : Type} (a : A) : (a = a) ↔ true :=