Commit 1a041014 by Guillaume Melquiond

### Factored proofs a bit.

parent 7a9b8478
 ... ... @@ -57,20 +57,35 @@ now apply Hr with (3 := Rle_refl x). now apply Hr with (3 := Rle_refl x). Qed. Theorem Rnd_DN_pt_monotone : forall F : R -> Prop, rounding_pred_monotone (Rnd_DN_pt F). Proof. intros F x y f g (Hx1,(Hx2,_)) (Hy1,(_,Hy2)) Hxy. apply Hy2. apply Hx1. now apply Rle_trans with (2 := Hxy). Qed. Theorem Rnd_DN_monotone : forall F : R -> Prop, forall rnd : R -> R, Rnd_DN F rnd -> MonotoneP rnd. Proof. intros F rnd Hr x y Hxy. now eapply Rnd_DN_pt_monotone. Qed. Theorem Rnd_DN_pt_unicity : forall F : R -> Prop, forall x f1 f2 : R, Rnd_DN_pt F x f1 -> Rnd_DN_pt F x f2 -> f1 = f2. Proof. intros F x f1 f2 H1 H2. apply Rle_antisym. eapply H2. now eapply H1. now eapply H1. eapply H1. now eapply H2. now eapply H2. intros F. apply rounding_unicity. apply Rnd_DN_pt_monotone. Qed. Theorem Rnd_DN_unicity : ... ... @@ -83,20 +98,35 @@ intros F rnd1 rnd2 H1 H2 x. now eapply Rnd_DN_pt_unicity. Qed. Theorem Rnd_UP_pt_monotone : forall F : R -> Prop, rounding_pred_monotone (Rnd_UP_pt F). Proof. intros F x y f g (Hx1,(_,Hx2)) (Hy1,(Hy2,_)) Hxy. apply Hx2. apply Hy1. now apply Rle_trans with (1 := Hxy). Qed. Theorem Rnd_UP_monotone : forall F : R -> Prop, forall rnd : R -> R, Rnd_UP F rnd -> MonotoneP rnd. Proof. intros F rnd Hr x y Hxy. now eapply Rnd_UP_pt_monotone. Qed. Theorem Rnd_UP_pt_unicity : forall F : R -> Prop, forall x f1 f2 : R, Rnd_UP_pt F x f1 -> Rnd_UP_pt F x f2 -> f1 = f2. Proof. intros F x f1 f2 H2 H1. apply Rle_antisym. eapply H2. now eapply H1. now eapply H1. eapply H1. now eapply H2. now eapply H2. intros F. apply rounding_unicity. apply Rnd_UP_pt_monotone. Qed. Theorem Rnd_UP_unicity : ... ... @@ -171,28 +201,6 @@ rewrite Ropp_involutive. apply H1. Qed. Theorem Rnd_DN_pt_monotone : forall F : R -> Prop, forall x y f g : R, Rnd_DN_pt F x f -> Rnd_DN_pt F y g -> x <= y -> f <= g. Proof. intros F x y f g (Hx1,(Hx2,_)) (Hy1,(_,Hy2)) Hxy. apply Hy2. apply Hx1. now apply Rle_trans with (2 := Hxy). Qed. Theorem Rnd_DN_monotone : forall F : R -> Prop, forall rnd : R -> R, Rnd_DN F rnd -> MonotoneP rnd. Proof. intros F rnd Hr x y Hxy. now eapply Rnd_DN_pt_monotone. Qed. Theorem Rnd_DN_pt_idempotent : forall F : R -> Prop, forall x f : R, ... ... @@ -221,28 +229,6 @@ intros x Hx. now apply Rnd_DN_pt_idempotent with (2 := Hx). Qed. Theorem Rnd_UP_pt_monotone : forall F : R -> Prop, forall x y f g : R, Rnd_UP_pt F x f -> Rnd_UP_pt F y g -> x <= y -> f <= g. Proof. intros F x y f g (Hx1,(_,Hx2)) (Hy1,(Hy2,_)) Hxy. apply Hx2. apply Hy1. now apply Rle_trans with (1 := Hxy). Qed. Theorem Rnd_UP_monotone : forall F : R -> Prop, forall rnd : R -> R, Rnd_UP F rnd -> MonotoneP rnd. Proof. intros F rnd Hr x y Hxy. now eapply Rnd_UP_pt_monotone. Qed. Theorem Rnd_UP_pt_idempotent : forall F : R -> Prop, forall x f : R, ... ...
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!