Commit 50b9555d by Ralf Jung Committed by Robbert Krebbers

### add decide_left, decide_right

parent cab3033b
 ... @@ -36,6 +36,11 @@ Lemma decide_iff {A} P Q `{Decision P, Decision Q} (x y : A) : ... @@ -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). (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. 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 (** The tactic [destruct_decide] destructs a sumbool [dec]. If one of the components is double negated, it will try to remove the double negation. *) components is double negated, it will try to remove the double negation. *) Tactic Notation "destruct_decide" constr(dec) "as" ident(H) := Tactic Notation "destruct_decide" constr(dec) "as" ident(H) := ... ...
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