diff options
Diffstat (limited to 'theories/ZArith/Zcomplements.v')
| -rw-r--r-- | theories/ZArith/Zcomplements.v | 9 |
1 files changed, 5 insertions, 4 deletions
diff --git a/theories/ZArith/Zcomplements.v b/theories/ZArith/Zcomplements.v index b4163ef99..a5e710504 100644 --- a/theories/ZArith/Zcomplements.v +++ b/theories/ZArith/Zcomplements.v @@ -53,10 +53,11 @@ Theorem Z_lt_abs_rec : forall n:Z, P n. Proof. intros P HP p. - set (Q := fun z => 0 <= z -> P z * P (- z)) in *. - cut (Q (Z.abs p)); [ intros | apply (Z_lt_rec Q); auto with zarith ]. - elim (Zabs_dec p); intro eq; rewrite eq; elim H; auto with zarith. - unfold Q; clear Q; intros. + set (Q := fun z => 0 <= z -> P z * P (- z)). + cut (Q (Z.abs p)); [ intros H | apply (Z_lt_rec Q); auto with zarith ]. + elim (Zabs_dec p); intro eq; rewrite eq; + elim H; auto with zarith. + intros x H; subst Q. split; apply HP. rewrite Z.abs_eq; auto; intros. elim (H (Z.abs m)); intros; auto with zarith. |