Commit d8ce723c authored by Guillaume Melquiond's avatar Guillaume Melquiond

Remove pred_eq_opp_succ_opp and succ_eq_opp_pred_opp.

parent 87c28ab4
......@@ -327,6 +327,7 @@ Qed.
Theorem Rnd_NE_pt_round :
round_pred Rnd_NE_pt.
Proof.
split.
apply Rnd_NE_pt_total.
apply Rnd_NE_pt_monotone.
......
......@@ -175,8 +175,6 @@ now apply Rabs_pos_lt.
now apply generic_format_abs.
Qed.
(* was ulp_DN_UP *)
Theorem round_UP_DN_ulp :
forall x, ~ F x ->
round beta fexp Zceil x = (round beta fexp Zfloor x + ulp x)%R.
......@@ -320,7 +318,7 @@ rewrite <- ulp_bpow.
apply H.
Qed.
Theorem ulp_le_pos :
Lemma ulp_le_pos :
forall { Hm : Monotone_exp fexp },
forall x y: R,
(0 <= x)%R -> (x <= y)%R ->
......@@ -395,30 +393,18 @@ intros x Hx; unfold succ.
now rewrite Rle_bool_true.
Qed.
Lemma pred_eq_opp_succ_opp :
forall x, pred x = (- succ (-x))%R.
Proof.
reflexivity.
Qed.
Lemma succ_eq_opp_pred_opp :
forall x, succ x = (- pred (-x))%R.
Proof.
intros x; unfold pred.
now rewrite 2!Ropp_involutive.
Qed.
Lemma succ_opp :
Theorem succ_opp :
forall x, succ (-x) = (- pred x)%R.
Proof.
intros x; rewrite succ_eq_opp_pred_opp.
now rewrite Ropp_involutive.
intros x.
now apply sym_eq, Ropp_involutive.
Qed.
Lemma pred_opp :
Theorem pred_opp :
forall x, pred (-x) = (- succ x)%R.
Proof.
intros x; rewrite pred_eq_opp_succ_opp.
intros x.
unfold pred.
now rewrite Ropp_involutive.
Qed.
......@@ -1540,7 +1526,7 @@ rewrite <- Ropp_0 at 1.
apply pred_opp.
Qed.
Theorem pred_succ_aux :
Lemma pred_succ_aux :
forall x, F x -> (0 < x)%R ->
pred (succ x) = x.
Proof.
......@@ -1572,8 +1558,8 @@ now apply succ_pred_aux.
rewrite <- Hx.
rewrite pred_0, succ_opp, pred_ulp_0.
apply Ropp_0.
rewrite pred_eq_opp_succ_opp, succ_opp.
rewrite pred_succ_aux.
unfold pred.
rewrite succ_opp, pred_succ_aux.
apply Ropp_involutive.
now apply generic_format_opp.
now apply Ropp_0_gt_lt_contravar.
......@@ -2003,12 +1989,16 @@ apply Rle_lt_trans with (2 := Hxy).
apply pred_le_id.
Qed.
Theorem succ_le: forall x y,
F x -> F y -> (x <= y)%R -> (succ x <= succ y)%R.
Theorem succ_le :
forall x y, F x -> F y -> (x <= y)%R ->
(succ x <= succ y)%R.
Proof.
intros x y Fx Fy Hxy.
rewrite 2!succ_eq_opp_pred_opp.
apply Ropp_le_contravar, pred_le; try apply generic_format_opp; try assumption.
apply Ropp_le_cancel.
rewrite <- 2!pred_opp.
apply pred_le.
now apply generic_format_opp.
now apply generic_format_opp.
now apply Ropp_le_contravar.
Qed.
......
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