proposition: Theorem abs_subset : forall x : R, forall xi zi : FF, ABS x xi -> abs_subset_helper xi zi = true -> ABS x zi.
proof: Proof. intros x xi zi (Hx1,Hx2) Hb. generalize (andb_prop _ _ Hb). clear Hb. intros (Hb,H3). generalize (andb_prop _ _ Hb). clear Hb. intros (H1,H2). generalize (Fpos0_correct _ H1). clear H1. intro H1. generalize (Fle2_correct _ _ H2). clear H2. intro H2. generalize (Fle2_correct _ _ H3). clear H3. intro H3. split. exact H1. apply IRsubset with (1 := H2) (2 := H3) (3 := Hx2). Qed.
imports: Gappa_common Gappa_pred_nzr