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Commit 89a5e9bc authored by Ralf Jung's avatar Ralf Jung
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simplify proofs even more

parent 82b3e17d
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1 merge request!81add inverses of bool_decide_{true,false}
...@@ -121,13 +121,9 @@ Lemma bool_decide_iff (P Q : Prop) `{Decision P, Decision Q} : ...@@ -121,13 +121,9 @@ Lemma bool_decide_iff (P Q : Prop) `{Decision P, Decision Q} :
Proof. repeat case_bool_decide; tauto. Qed. Proof. repeat case_bool_decide; tauto. Qed.
Lemma bool_decide_true_2 P `{!Decision P}: bool_decide P = true P. Lemma bool_decide_true_2 P `{!Decision P}: bool_decide P = true P.
Proof. intros Heq. eapply bool_decide_unpack. rewrite Heq. exact I. Qed. Proof. case_bool_decide; auto || discriminate. Qed.
Lemma bool_decide_false_2 P `{!Decision P}: bool_decide P = false ¬P. Lemma bool_decide_false_2 P `{!Decision P}: bool_decide P = false ¬P.
Proof. Proof. case_bool_decide; auto || discriminate. Qed.
intros Heq HP. assert (HP': bool_decide P).
{ apply bool_decide_spec. assumption. }
case_bool_decide; auto || discriminate.
Qed.
(** * Decidable Sigma types *) (** * Decidable Sigma types *)
(** Leibniz equality on Sigma types requires the equipped proofs to be (** Leibniz equality on Sigma types requires the equipped proofs to be
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