diff options
Diffstat (limited to 'theories/Reals/Exp_prop.v')
| -rw-r--r-- | theories/Reals/Exp_prop.v | 12 |
1 files changed, 4 insertions, 8 deletions
diff --git a/theories/Reals/Exp_prop.v b/theories/Reals/Exp_prop.v index 569518f7b..e9de24898 100644 --- a/theories/Reals/Exp_prop.v +++ b/theories/Reals/Exp_prop.v @@ -439,20 +439,16 @@ Proof. repeat rewrite <- Rmult_assoc. rewrite <- Rinv_r_sym. rewrite Rmult_1_l. - replace (INR N * INR N) with (Rsqr (INR N)); [ idtac | reflexivity ]. - rewrite Rmult_assoc. - rewrite Rmult_comm. - replace 4 with (Rsqr 2); [ idtac | ring_Rsqr ]. + change 4 with (Rsqr 2). rewrite <- Rsqr_mult. apply Rsqr_incr_1. - replace 2 with (INR 2). - rewrite <- mult_INR; apply H1. - reflexivity. + change 2 with (INR 2). + rewrite Rmult_comm, <- mult_INR; apply H1. left; apply lt_INR_0; apply H. left; apply Rmult_lt_0_compat. - prove_sup0. apply lt_INR_0; apply div2_not_R0. apply lt_n_S; apply H. + now apply IZR_lt. cut (1 < S N)%nat. intro; unfold Rsqr; apply prod_neq_R0; apply not_O_INR; intro; assert (H4 := div2_not_R0 _ H2); rewrite H3 in H4; |