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Diffstat (limited to 'lib/Coqlib.v')
| -rw-r--r-- | lib/Coqlib.v | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/lib/Coqlib.v b/lib/Coqlib.v index 0fc8613c..184fe28f 100644 --- a/lib/Coqlib.v +++ b/lib/Coqlib.v @@ -846,3 +846,34 @@ Proof. intros P Q a. destruct a; simpl. auto. congruence. Qed. +Section DECIDABLE_EQUALITY. + +Variable A: Set. +Variable dec_eq: forall (x y: A), {x=y} + {x<>y}. +Variable B: Set. + +Lemma dec_eq_true: + forall (x: A) (ifso ifnot: B), + (if dec_eq x x then ifso else ifnot) = ifso. +Proof. + intros. destruct (dec_eq x x). auto. congruence. +Qed. + +Lemma dec_eq_false: + forall (x y: A) (ifso ifnot: B), + x <> y -> (if dec_eq x y then ifso else ifnot) = ifnot. +Proof. + intros. destruct (dec_eq x y). congruence. auto. +Qed. + +Lemma dec_eq_sym: + forall (x y: A) (ifso ifnot: B), + (if dec_eq x y then ifso else ifnot) = + (if dec_eq y x then ifso else ifnot). +Proof. + intros. destruct (dec_eq x y). + subst y. rewrite dec_eq_true. auto. + rewrite dec_eq_false; auto. +Qed. + +End DECIDABLE_EQUALITY. |