Library general_tactics

Ltac ex_elim H x := elim H; intros x ; intro; clear H.

Ltac DecompEx H P := elim H;intro P;intro;clear H.

Ltac DecompExAnd H P :=
  elim H;intro P;let id:=fresh in
(intro id;decompose [and] id;clear id;clear H).

Ltac exist_hyp t := match goal with
  | H1:t |- _ => idtac
 end.

Ltac hyp_of_type t := match goal with
  | H1:t |- _ => H1
end.

Ltac clean_duplicated_hyps :=
  repeat match goal with
      | H:?X1 |- _ => clear H; exist_hyp X1
end.

Ltac suppose H := cut H;[intro|idtac].

Ltac not_exist_hyp t := match goal with
  | H1:t |- _ => fail 2
 end || idtac.

Ltac DecompAndAll :=
 repeat
 match goal with
   | H:(?X1 /\ ?X2) |- _ => decompose [and] H;clear H
end.

Ltac assert_if_not_exist H :=
  not_exist_hyp H;assert H.


Ltac absurde :=
match goal with
   |H : (?X <> ?X) |- _ => apply False_ind; apply H; reflexivity
end.

Ltac spliter := repeat
match goal with
   | H:(?X1 /\ ?X2) |- _ => induction H
end.

Ltac ex_and H x := ex_elim H x; spliter.