diff options
Diffstat (limited to 'theories/Reals/ArithProp.v')
| -rw-r--r-- | theories/Reals/ArithProp.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Reals/ArithProp.v b/theories/Reals/ArithProp.v index 7d9fff276..67584f775 100644 --- a/theories/Reals/ArithProp.v +++ b/theories/Reals/ArithProp.v @@ -106,7 +106,7 @@ Proof. split. ring. unfold k0; case (Rcase_abs y) as [Hlt|Hge]. - assert (H0 := archimed (x / - y)); rewrite <- Z_R_minus; change (IZR 1) with 1; + assert (H0 := archimed (x / - y)); rewrite <- Z_R_minus; simpl; unfold Rminus. replace (- ((1 + - IZR (up (x / - y))) * y)) with ((IZR (up (x / - y)) - 1) * y); [ idtac | ring ]. @@ -140,10 +140,10 @@ Proof. rewrite <- Ropp_mult_distr_r_reverse; rewrite (Ropp_inv_permute _ H); elim H0; unfold Rdiv; intros H1 _; exact H1. apply Ropp_neq_0_compat; assumption. - assert (H0 := archimed (x / y)); rewrite <- Z_R_minus; change (IZR 1) with 1; + assert (H0 := archimed (x / y)); rewrite <- Z_R_minus; simpl; cut (0 < y). intro; unfold Rminus; - replace (- ((IZR (up (x / y)) + -1) * y)) with ((1 - IZR (up (x / y))) * y); + replace (- ((IZR (up (x / y)) + -(1)) * y)) with ((1 - IZR (up (x / y))) * y); [ idtac | ring ]. split. apply Rmult_le_reg_l with (/ y). |