Commit 1574e8c2 by Guillaume Melquiond

### Added theorems about reflexivity of standard predicates.

parent c8016fa9
 ... ... @@ -201,6 +201,18 @@ rewrite Ropp_involutive. apply H1. Qed. Theorem Rnd_DN_pt_refl : forall F : R -> Prop, forall x : R, F x -> Rnd_DN_pt F x x. Proof. intros F x Hx. repeat split. exact Hx. apply Rle_refl. now intros. Qed. Theorem Rnd_DN_pt_idempotent : forall F : R -> Prop, forall x f : R, ... ... @@ -229,6 +241,18 @@ intros x Hx. now apply Rnd_DN_pt_idempotent with (2 := Hx). Qed. Theorem Rnd_UP_pt_refl : forall F : R -> Prop, forall x : R, F x -> Rnd_UP_pt F x x. Proof. intros F x Hx. repeat split. exact Hx. apply Rle_refl. now intros. Qed. Theorem Rnd_UP_pt_idempotent : forall F : R -> Prop, forall x f : R, ... ... @@ -551,6 +575,20 @@ rewrite Hxy. apply Rle_refl. Qed. Theorem Rnd_N_pt_refl : forall F : R -> Prop, forall x : R, F x -> Rnd_N_pt F x x. Proof. intros F x Hx. repeat split. exact Hx. intros g _. unfold Rminus at 1. rewrite Rplus_opp_r, Rabs_R0. apply Rabs_pos. Qed. Theorem Rnd_N_pt_idempotent : forall F : R -> Prop, forall x f : R, ... ... @@ -884,6 +922,20 @@ intros F rnd Hr x y Hxy. now apply Rnd_NA_pt_monotone with F. Qed. Theorem Rnd_NA_pt_refl : forall F : R -> Prop, forall x : R, F x -> Rnd_NA_pt F x x. Proof. intros F x Hx. split. now apply Rnd_N_pt_refl. intros f Hxf. apply Req_le. apply f_equal. now apply Rnd_N_pt_idempotent with (1 := Hxf). Qed. Theorem Rnd_NA_pt_idempotent : forall F : R -> Prop, forall x f : R, ... ...
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