Goal:
  
  ============================
   (forall (A : Type) (R : ReflectEq A) (x y : A), false = (x == y) -> x <> y)


DEBUG:Going to execute:
simpl; intros; Tactics.destruct_all_rec_calls;
            repeat (Tactics.destruct_conjs; simpl proj1_sig in *); subst *