diff options
Diffstat (limited to 'theories/Reals/Rfunctions.v')
| -rw-r--r-- | theories/Reals/Rfunctions.v | 15 |
1 files changed, 8 insertions, 7 deletions
diff --git a/theories/Reals/Rfunctions.v b/theories/Reals/Rfunctions.v index 5eb34324e..604160834 100644 --- a/theories/Reals/Rfunctions.v +++ b/theories/Reals/Rfunctions.v @@ -489,16 +489,16 @@ Lemma pow_Rabs : forall (x:R) (n:nat), x ^ n <= Rabs x ^ n. Proof. intros; induction n as [| n Hrecn]. right; reflexivity. - simpl; case (Rcase_abs x); intro. + simpl; destruct (Rcase_abs x) as [Hlt|Hle]. apply Rle_trans with (Rabs (x * x ^ n)). apply RRle_abs. rewrite Rabs_mult. apply Rmult_le_compat_l. apply Rabs_pos. - right; symmetry ; apply RPow_abs. - pattern (Rabs x) at 1; rewrite (Rabs_right x r); + right; symmetry; apply RPow_abs. + pattern (Rabs x) at 1; rewrite (Rabs_right x Hle); apply Rmult_le_compat_l. - apply Rge_le; exact r. + apply Rge_le; exact Hle. apply Hrecn. Qed. @@ -741,10 +741,11 @@ Qed. Lemma R_dist_sym : forall x y:R, R_dist x y = R_dist y x. Proof. unfold R_dist; intros; split_Rabs; try ring. - generalize (Ropp_gt_lt_0_contravar (y - x) r); intro; - rewrite (Ropp_minus_distr y x) in H; generalize (Rlt_asym (x - y) 0 r0); +Show. + generalize (Ropp_gt_lt_0_contravar (y - x) Hlt0); intro; + rewrite (Ropp_minus_distr y x) in H; generalize (Rlt_asym (x - y) 0 Hlt); intro; unfold Rgt in H; exfalso; auto. - generalize (minus_Rge y x r); intro; generalize (minus_Rge x y r0); intro; + generalize (minus_Rge y x Hge0); intro; generalize (minus_Rge x y Hge); intro; generalize (Rge_antisym x y H0 H); intro; rewrite H1; ring. Qed. |