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.