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(* Copyright 2021 Pierre Courtieu
This file is part of LibHyps. It is distributed under the MIT
"expat license". You should have recieved a LICENSE file with it. *)
(** ** A specific variant of decompose. Which decomposes all logical connectives. *)
Ltac decomp_logicals h :=
idtac;match type of h with
| @ex _ (fun x => _) => let x' := fresh x in let h1 := fresh in destruct h as [x' h1]; decomp_logicals h1
| @sig _ (fun x => _) => let x' := fresh x in let h1 := fresh in destruct h as [x' h1]; decomp_logicals h1
| @sig2 _ (fun x => _) (fun _ => _) => let x' := fresh x in
let h1 := fresh in
let h2 := fresh in
destruct h as [x' h1 h2];
decomp_logicals h1;
decomp_logicals h2
| @sigT _ (fun x => _) => let x' := fresh x in let h1 := fresh in destruct h as [x' h1]; decomp_logicals h1
| @sigT2 _ (fun x => _) (fun _ => _) => let x' := fresh x in
let h1 := fresh in
let h2 := fresh in
destruct h as [x' h1 h2]; decomp_logicals h1; decomp_logicals h2
| and _ _ => let h1 := fresh in let h2 := fresh in destruct h as [h1 h2]; decomp_logicals h1; decomp_logicals h2
| iff _ _ => let h1 := fresh in let h2 := fresh in destruct h as [h1 h2]; decomp_logicals h1; decomp_logicals h2
| or _ _ => let h' := fresh in destruct h as [h' | h']; [decomp_logicals h' | decomp_logicals h' ]
| _ => idtac
end.
(*
Lemma foo: (IF_then_else False True False) -> False.
Proof.
intros H.
decomp_logicals H.
Admitted.
Lemma foo2 : { aa:False & True } -> False.
Proof.
intros H.
decomp_logicals H.
Admitted.
Lemma foo3 : { aa:False & True & False } -> False.
Proof.
intros H.
decomp_logicals H.
Abort.
*)
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