Commit 39cf7e2e authored by Guillaume Melquiond's avatar Guillaume Melquiond

Moved opposites to goals.

parent e37bc5ec
......@@ -711,9 +711,10 @@ Theorem generic_UP_pt :
Rnd_UP_pt generic_format x (rounding ZrndUP x).
Proof.
intros x.
rewrite <- (Ropp_involutive x).
rewrite rounding_UP_opp.
apply Rnd_DN_UP_pt_sym.
apply generic_format_satisfies_any.
rewrite <- rounding_DN_opp.
apply generic_DN_pt.
Qed.
......
......@@ -143,44 +143,42 @@ Theorem Rnd_DN_UP_pt_sym :
forall F : R -> Prop,
( forall x, F x -> F (- x) ) ->
forall x f : R,
Rnd_DN_pt F (-x) (-f) -> Rnd_UP_pt F x f.
Rnd_DN_pt F x f -> Rnd_UP_pt F (-x) (-f).
Proof.
intros F HF x f H.
rewrite <- (Ropp_involutive f).
repeat split.
apply HF.
apply H.
apply Ropp_le_cancel.
rewrite Ropp_involutive.
apply Ropp_le_contravar.
apply H.
intros.
apply Ropp_le_cancel.
rewrite Ropp_involutive.
intros g Hg.
rewrite <- (Ropp_involutive g).
intros Hxg.
apply Ropp_le_contravar.
apply H.
now apply HF.
now apply Ropp_le_contravar.
now apply Ropp_le_cancel.
Qed.
Theorem Rnd_UP_DN_pt_sym :
forall F : R -> Prop,
( forall x, F x -> F (- x) ) ->
forall x f : R,
Rnd_UP_pt F (-x) (-f) -> Rnd_DN_pt F x f.
Rnd_UP_pt F x f -> Rnd_DN_pt F (-x) (-f).
Proof.
intros F HF x f H.
rewrite <- (Ropp_involutive f).
repeat split.
apply HF.
apply H.
apply Ropp_le_cancel.
rewrite Ropp_involutive.
apply Ropp_le_contravar.
apply H.
intros.
apply Ropp_le_cancel.
rewrite Ropp_involutive.
intros g Hg.
rewrite <- (Ropp_involutive g).
intros Hxg.
apply Ropp_le_contravar.
apply H.
now apply HF.
now apply Ropp_le_contravar.
now apply Ropp_le_cancel.
Qed.
Theorem Rnd_DN_UP_sym :
......@@ -195,9 +193,9 @@ rewrite <- (Ropp_involutive (rnd1 (-x))).
apply f_equal.
apply (Rnd_UP_unicity F (fun x => - rnd1 (-x))) ; trivial.
intros y.
pattern y at 1 ; rewrite <- Ropp_involutive.
apply Rnd_DN_UP_pt_sym.
apply HF.
rewrite Ropp_involutive.
apply H1.
Qed.
......@@ -1293,9 +1291,10 @@ split.
intros x.
destruct (proj1 (satisfies_any_imp_DN F Hany) (-x)) as (f, Hf).
exists (-f).
rewrite <- (Ropp_involutive x).
apply Rnd_DN_UP_pt_sym.
apply Hany.
now rewrite Ropp_involutive.
exact Hf.
apply Rnd_UP_pt_monotone.
Qed.
......
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