Commit f26588e6 authored by BOLDO Sylvie's avatar BOLDO Sylvie


parent 69a33aa7
......@@ -883,26 +883,30 @@ Qed.
Theorem rounding_DN_pred :
forall x, (0 < x)%R -> F x ->
forall x, (0 < pred x)%R -> F x ->
forall eps, (0 < eps <= ulp (pred x))%R ->
rounding beta fexp ZrndDN (x - eps) = pred x.
intros x Hx Fx eps Heps.
intros x Hpx Fx eps Heps.
assert (Hx:(0 < x)%R).
apply Rlt_trans with (1:=Hpx).
apply pred_lt.
replace (x-eps)%R with (pred x + (ulp (pred x)-eps))%R.
2: pattern x rewrite <- (Fpred_ulp x).
2: pattern x at 3; rewrite <- (pred_ulp x); trivial.
2: ring.
2: now apply Rgt_not_eq.
rewrite rounding_DN_succ; trivial.
apply Fpred_ulp; trivial.
apply Rlt_trans with (1:=Hx).
apply Fpred_lt.
auto with real.
apply Fpred_format; trivial.
apply Rlt_trans with (1:=Hx).
apply Fpred_lt.
now apply format_pred.
apply Rle_0_minus.
now apply Heps.
rewrite <- Rplus_0_r.
apply Rplus_lt_compat_l.
rewrite <- Ropp_0.
apply Ropp_lt_contravar.
now apply Heps.
Theorem succ_lt_le:
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