refactor(library/logic): use new K-like reduction to simplify some proofs

library/logic/cast.lean

@@ -16,8 +16,7 @@ theorem cast_proof_irrel {A B : Type} (H₁ H₂ : A = B) (a : A) : cast H₁ a
 rfl
 
 theorem cast_eq {A : Type} (H : A = A) (a : A) : cast H a = a :=
-calc cast H a = cast (eq.refl A) a : rfl
-         ...  = a                  : rfl
+rfl
 
 inductive heq.{l} {A : Type.{l}} (a : A) : Π {B : Type.{l}}, B → Prop :=
 refl : heq a a

library/logic/eq.lean

@@ -26,7 +26,7 @@ section
   variables {A : Type}
   variables {a b c : A}
   theorem id_refl (H₁ : a = a) : H₁ = (eq.refl a) :=
-  !proof_irrel
+  rfl
 
   theorem irrel (H₁ H₂ : a = b) : H₁ = H₂ :=
   !proof_irrel
@@ -58,7 +58,7 @@ namespace eq
   eq.rec (λH₁ : a = a, show B a H₁, from H₂) H₁ H₁
 
   theorem rec_on_id {A : Type} {a : A} {B : Πa' : A, a = a' → Type} (H : a = a) (b : B a H) : rec_on H b = b :=
-  refl (rec_on rfl b)
+  rfl
 
   theorem rec_on_constant {A : Type} {a a' : A} {B : Type} (H : a = a') (b : B) : rec_on H b = b :=
   rec_on H (λ(H' : a = a), rec_on_id H' b) H
@@ -72,7 +72,7 @@ namespace eq
   rec_on H (λ(H : a = a) (H' : f a = f a), rec_on_id H b ⬝ rec_on_id H' b⁻¹) H H'
 
   theorem rec_id {A : Type} {a : A} {B : A → Type} (H : a = a) (b : B a) : rec b H = b :=
-  id_refl H⁻¹ ▸ refl (eq.rec b (refl a))
+  rfl
 
   theorem rec_on_compose {A : Type} {a b c : A} {P : A → Type} (H₁ : a = b) (H₂ : b = c)
           (u : P a) :