Library Float.sTactic



Theorem Contradict1 : forall a b : Prop, b -> (a -> ~ b) -> ~ a.
intuition.
Qed.

Theorem Contradict2 : forall a b : Prop, b -> ~ b -> a.
intuition.
Qed.

Theorem Contradict3 : forall a : Prop, a -> ~ ~ a.
auto.
Qed.

Ltac Contradict name :=
  (apply (fun a : Prop => Contradict1 a _ name); clear name; intros name) ||
    (apply (fun a : Prop => Contradict2 a _ name); clear name);
   try apply Contradict3.


Ltac CaseEq name :=
  generalize (refl_equal name); pattern name at -1 in |- *; case name.

Ltac Casec name := case name; clear name.

Ltac Elimc name := elim name; clear name.