diff options
Diffstat (limited to 'theories/Reals/Rcomplete.v')
| -rw-r--r-- | theories/Reals/Rcomplete.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Reals/Rcomplete.v b/theories/Reals/Rcomplete.v index 53624cbb2d..5887e8ef06 100644 --- a/theories/Reals/Rcomplete.v +++ b/theories/Reals/Rcomplete.v @@ -26,8 +26,8 @@ Open Local Scope R_scope. Theorem R_complete : forall Un:nat -> R, Cauchy_crit Un -> sigT (fun l:R => Un_cv Un l). intros. -pose (Vn := sequence_minorant Un (cauchy_min Un H)). -pose (Wn := sequence_majorant Un (cauchy_maj Un H)). +set (Vn := sequence_minorant Un (cauchy_min Un H)). +set (Wn := sequence_majorant Un (cauchy_maj Un H)). assert (H0 := maj_cv Un H). fold Wn in H0. assert (H1 := min_cv Un H). @@ -118,7 +118,7 @@ elim (p0 (eps / 5) H3); intros N2 H5. unfold Cauchy_crit in H. unfold R_dist in H. elim (H (eps / 5) H3); intros N3 H6. -pose (N := max (max N1 N2) N3). +set (N := max (max N1 N2) N3). apply Rle_lt_trans with (Rabs (x - Wn N) + Rabs (Wn N - x0)). replace (x - x0) with (x - Wn N + (Wn N - x0)); [ apply Rabs_triang | ring ]. apply Rle_lt_trans with |