proposition: Theorem add : forall x y : R, forall xi yi zi : FF, BND x xi -> BND y yi -> add_helper xi yi zi = true -> BND (x + y) zi.
proof: Proof. intros x y xi yi zi Hx Hy Hb. generalize (andb_prop _ _ Hb). clear Hb. intros (H1,H2). generalize (Fle2_correct _ _ H1). rewrite Fplus2_correct. clear H1. intro H1. generalize (Fle2_correct _ _ H2). rewrite Fplus2_correct. clear H2. intro H2. apply IRplus with (1 := H1) (2 := H2) (3 := Hx) (4 := Hy). Qed.
imports: Gappa_common Gappa_decimal