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Diffstat (limited to 'lib/Coqlib.v')
| -rw-r--r-- | lib/Coqlib.v | 21 |
1 files changed, 21 insertions, 0 deletions
diff --git a/lib/Coqlib.v b/lib/Coqlib.v index b936b9b..ce5d94e 100644 --- a/lib/Coqlib.v +++ b/lib/Coqlib.v @@ -559,6 +559,16 @@ Proof. Defined. Global Opaque Zdivide_dec. +Lemma Zdivide_interval: + forall a b c, + 0 < c -> 0 <= a < b -> (c | a) -> (c | b) -> 0 <= a <= b - c. +Proof. + intros. destruct H1 as [x EQ1]. destruct H2 as [y EQ2]. subst. destruct H0. + split. omega. exploit Zmult_lt_reg_r; eauto. intros. + replace (y * c - c) with ((y - 1) * c) by ring. + apply Zmult_le_compat_r; omega. +Qed. + (** Conversion from [Z] to [nat]. *) Definition nat_of_Z: Z -> nat := Z.to_nat. @@ -1250,6 +1260,17 @@ Proof. intros. unfold proj_sumbool. destruct a. auto. contradiction. Qed. +Ltac InvBooleans := + match goal with + | [ H: _ && _ = true |- _ ] => + destruct (andb_prop _ _ H); clear H; InvBooleans + | [ H: _ || _ = false |- _ ] => + destruct (orb_false_elim _ _ H); clear H; InvBooleans + | [ H: proj_sumbool ?x = true |- _ ] => + generalize (proj_sumbool_true _ H); clear H; intro; InvBooleans + | _ => idtac + end. + Section DECIDABLE_EQUALITY. Variable A: Type. |