Commit 3d44b057 authored by BOLDO Sylvie's avatar BOLDO Sylvie

WIP version

parent 2f0e650e
......@@ -33,32 +33,31 @@ now apply H.
Qed.
Theorem implies_MinOrMax_le:
Theorem implies_DN_lt_ulp_f:
forall x f, format f ->
(f <= x)%R ->
(Rabs (f-x) < ulp x)%R ->
MinOrMax x f.
(0 < f <= x)%R ->
(Rabs (f-x) < ulp f)%R ->
(f = rounding beta (FLX_exp prec) ZrndDN x)%R.
intros x f Hf Hxf1 Hxf2.
left; apply sym_eq.
apply Rnd_DN_pt_unicity with format x.
apply generic_DN_pt.
now apply FLX_exp_correct.
split;[assumption|idtac].
split;[assumption|idtac].
intros g Hg Hxg.
case (Rle_or_lt g f); trivial; intros Hfg.
contradict Hxf2.
apply Rle_not_lt.
rewrite Rabs_left1.
2: apply Rle_minus; assumption.
replace (-(f-x))%R with ((x-g)+(g-f))%R by ring.
rewrite <- (Rplus_0_l (ulp x)).
apply Rplus_le_compat.
apply Rle_0_minus; assumption.
(*succ_lt_le:*)
Admitted.
apply sym_eq.
replace x with (f+-(f-x))%R by ring.
apply rounding_DN_succ; trivial.
apply Hxf1.
replace (- (f - x))%R with (Rabs (f-x)).
split; trivial; apply Rabs_pos.
rewrite Rabs_left1; trivial.
now apply Rle_minus.
Qed.
Theorem implies_DN_lt_ulp:
forall x f, format f ->
(0 < f <= x)%R ->
(Rabs (f-x) < ulp x)%R ->
(f = rounding beta (FLX_exp prec) ZrndDN x)%R.
intros x f Hf Hxf1 Hxf2.
apply implies_DN_lt_ulp_f; trivial.
Admitted.
Theorem implies_MinOrMax_quarter:
......
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