diff options
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/Reals/RiemannInt_SF.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Reals/RiemannInt_SF.v b/theories/Reals/RiemannInt_SF.v index d2c04f556..ef5d37bff 100644 --- a/theories/Reals/RiemannInt_SF.v +++ b/theories/Reals/RiemannInt_SF.v @@ -69,19 +69,19 @@ Proof. [ assumption | ring ] ]. assert (H11 : (0 <= up x)%Z). apply le_IZR; apply Rle_trans with x; [ apply H6 | left; assumption ]. - assert (H12 := IZN_var H11); elim H12; clear H12; intros; assert (H13 : E x). + assert (H12 := IZN_var H11); elim H12; clear H12; intros x0 H8; assert (H13 : E x). elim (classic (E x)); intro; try assumption. cut (forall y:R, E y -> y <= x - 1). - intro; assert (H14 := H5 _ H13); cut (x - 1 < x). - intro; elim (Rlt_irrefl _ (Rle_lt_trans _ _ _ H14 H15)). + intro H13; assert (H14 := H5 _ H13); cut (x - 1 < x). + intro H15; elim (Rlt_irrefl _ (Rle_lt_trans _ _ _ H14 H15)). apply Rminus_lt; replace (x - 1 - x) with (-1); [ idtac | ring ]; rewrite <- Ropp_0; apply Ropp_lt_gt_contravar; apply Rlt_0_1. - intros; assert (H14 := H4 _ H13); elim H14; intro; unfold E in H13; elim H13; - intros; elim H16; intros; apply Rplus_le_reg_l with 1. + intros y H13; assert (H14 := H4 _ H13); elim H14; intro H15; unfold E in H13; elim H13; + intros x1 H16; elim H16; intros H17 H18; apply Rplus_le_reg_l with 1. replace (1 + (x - 1)) with x; [ idtac | ring ]; rewrite <- H18; replace (1 + INR x1) with (INR (S x1)); [ idtac | rewrite S_INR; ring ]. cut (x = INR (pred x0)). - intro; rewrite H19; apply le_INR; apply lt_le_S; apply INR_lt; rewrite H18; + intro H19; rewrite H19; apply le_INR; apply lt_le_S; apply INR_lt; rewrite H18; rewrite <- H19; assumption. rewrite H10; rewrite H8; rewrite <- INR_IZR_INZ; replace 1 with (INR 1); [ idtac | reflexivity ]; rewrite <- minus_INR. |