diff options
Diffstat (limited to 'theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v')
| -rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v | 7 |
1 files changed, 3 insertions, 4 deletions
diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v index 7b90aa09e..6760cfc81 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v +++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v @@ -292,11 +292,10 @@ Proof. intros a b. zify. intros. apply Z_div_mod_eq_full; auto. Qed. -Theorem mod_upper_bound : forall a b, ~b==0 -> modulo a b < b. +Theorem mod_bound_pos : forall a b, 0<=a -> 0<b -> + 0 <= modulo a b /\ modulo a b < b. Proof. -intros a b. zify. intros. -destruct (Z_mod_lt [a] [b]); auto. -generalize (spec_pos b); auto with zarith. +intros a b. zify. apply Z.mod_bound_pos. Qed. (** Gcd *) |