Commit 46304c52 by Robbert Krebbers

### Misc prelude changes.

parent 472ccca0
 ... ... @@ -24,10 +24,10 @@ Lemma decide_rel_correct {A B} (R : A → B → Prop) `{∀ x y, Decision (R x y (x : A) (y : B) : decide_rel R x y = decide (R x y). Proof. done. Qed. Lemma decide_true {A} `{Decision P} (x y : A) : Lemma decide_True {A} `{Decision P} (x y : A) : P → (if decide P then x else y) = x. Proof. by destruct (decide P). Qed. Lemma decide_false {A} `{Decision P} (x y : A) : Lemma decide_False {A} `{Decision P} (x y : A) : ¬P → (if decide P then x else y) = y. Proof. by destruct (decide P). Qed. ... ...
 ... ... @@ -137,6 +137,13 @@ Tactic Notation "case_option_guard" "as" ident(Hx) := Tactic Notation "case_option_guard" := let H := fresh in case_option_guard as H. Lemma option_guard_True {A} (P : Prop) `{Decision P} (x : option A) : P → guard P; x = x. Proof. intros. by case_option_guard. Qed. Lemma option_guard_False {A} (P : Prop) `{Decision P} (x : option A) : ¬P → guard P; x = None. Proof. intros. by case_option_guard. Qed. Tactic Notation "simplify_option_equality" "by" tactic3(tac) := repeat match goal with | _ => progress (unfold default in *) ... ...
 ... ... @@ -30,10 +30,9 @@ Proof. destruct b; simpl; apply _. Qed. Lemma sig_eq_pi `(P : A → Prop) `{∀ x, ProofIrrel (P x)} (x y : sig P) : x = y ↔ `x = `y. Proof. split. * destruct x, y. apply proj1_sig_inj. * destruct x as [x Hx], y as [y Hy]; simpl; intros; subst. f_equal. apply proof_irrel. split; [by intros <- |]. destruct x as [x Hx], y as [y Hy]; simpl; intros; subst. f_equal. apply proof_irrel. Qed. Lemma exists_proj1_pi `(P : A → Prop) `{∀ x, ProofIrrel (P x)} ... ...
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