Commit 1c9e8581 authored by Ralf Jung's avatar Ralf Jung

add decide_left, decide_right

parent 2e3a9be0
Pipeline #3434 passed with stage
in 11 minutes and 26 seconds
......@@ -36,6 +36,11 @@ Lemma decide_iff {A} P Q `{Decision P, Decision Q} (x y : A) :
(P Q) (if decide P then x else y) = (if decide Q then x else y).
Proof. intros [??]. destruct (decide P), (decide Q); tauto. Qed.
Lemma decide_left`{Decision P, !ProofIrrel P} (HP : P) : decide P = left HP.
Proof. destruct (decide P) as [?|?]; [|contradiction]. f_equal. apply proof_irrel. Qed.
Lemma decide_right`{Decision P} `{!ProofIrrel (¬ P)} (HP : ¬ P) : decide P = right HP.
Proof. destruct (decide P) as [?|?]; [contradiction|]. f_equal. apply proof_irrel. Qed.
(** The tactic [destruct_decide] destructs a sumbool [dec]. If one of the
components is double negated, it will try to remove the double negation. *)
Tactic Notation "destruct_decide" constr(dec) "as" ident(H) :=
......
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