chore(builtin/kernel): cleanup

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/builtin/kernel.lean

@@ -113,12 +113,12 @@ theorem absurd_elim {a : Bool} (b : Bool) (H1 : a) (H2 : ¬ a) : b
 theorem not_imp_eliml {a b : Bool} (Hnab : ¬ (a → b)) : a
 := not_not_elim
       (have ¬ ¬ a :
-       λ Hna : ¬ a, absurd (have a → b     : λ Ha : a, absurd_elim b Ha Hna)
+          λ Hna : ¬ a, absurd (λ Ha : a, absurd_elim b Ha Hna)
                               Hnab)
 
 theorem not_imp_elimr {a b : Bool} (H : ¬ (a → b)) : ¬ b
-:= λ Hb : b, absurd (have a → b : λ Ha : a, Hb)
+:= λ Hb : b, absurd (λ Ha : a, Hb)
-                    (have ¬ (a → b) : H)
+                    H
 
 theorem resolve1 {a b : Bool} (H1 : a ∨ b) (H2 : ¬ a) : b
 := H1 H2
@@ -197,7 +197,8 @@ theorem boolext {a b : Bool} (Hab : a → b) (Hba : b → a) : a == b
            (λ Hbt : b == true,  false_elim (a == b) (subst (Hba (eqt_elim Hbt)) Haf))
            (λ Hbf : b == false, trans Haf (symm Hbf)))
 
-definition iff_intro {a b : Bool} (Hab : a → b) (Hba : b → a) := boolext Hab Hba
+theorem iff_intro {a b : Bool} (Hab : a → b) (Hba : b → a) : a == b
+:= boolext Hab Hba
 
 theorem eqt_intro {a : Bool} (H : a) : a == true
 := boolext (λ H1 : a, trivial)
@@ -209,7 +210,8 @@ theorem or_comm (a b : Bool) : (a ∨ b) == (b ∨ a)
 
 theorem or_assoc (a b c : Bool) : ((a ∨ b) ∨ c) == (a ∨ (b ∨ c))
 := boolext (λ H : (a ∨ b) ∨ c,
-                      or_elim H (λ H1 : a ∨ b, or_elim H1 (λ Ha : a, or_introl Ha (b ∨ c)) (λ Hb : b, or_intror a (or_introl Hb c)))
+                      or_elim H (λ H1 : a ∨ b, or_elim H1 (λ Ha : a, or_introl Ha (b ∨ c))
+                                                          (λ Hb : b, or_intror a (or_introl Hb c)))
                                 (λ Hc : c, or_intror a (or_intror b Hc)))
            (λ H : a ∨ (b ∨ c),
                       or_elim H (λ Ha : a, (or_introl (or_introl Ha b) c))