proposition: Theorem abs_of_bnd_o : forall x : R, forall xi zi : FF, BND x xi -> abs_of_bnd_o_helper xi zi = true -> ABS x zi.
proof: Proof. intros x xi zi Hx Hb. generalize (andb_prop _ _ Hb). clear Hb. intros (Hb,H3). generalize (andb_prop _ _ Hb). clear Hb. intros (H1,H2). generalize (Fis0_correct _ H1). clear H1. intro H1. generalize (Fle2_correct _ _ H2). clear H2. intro H2. generalize (Fle2_correct _ _ H3). rewrite Fopp2_correct. clear H3. intro H3. split. rewrite H1. apply Rle_refl. apply IRabs_o with (2 := H3) (3 := H2) (4 := Hx). rewrite H1. apply Rle_refl. Qed.
imports: Gappa_common Gappa_pred_nzr