proposition: Theorem mul_no : forall x y : R, forall xi yi zi : FF, BND x xi -> BND y yi -> mul_no_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 (Hb,H5). generalize (andb_prop _ _ Hb). clear Hb. intros (Hb,H4). generalize (andb_prop _ _ Hb). clear Hb. intros (Hb,H3). generalize (andb_prop _ _ Hb). clear Hb. intros (H1,H2). generalize (Fneg0_correct _ H1). clear H1. intro H1. generalize (Fneg0_correct _ H2). clear H2. intro H2. generalize (Fpos0_correct _ H3). clear H3. intro H3. generalize (Fle2_correct _ _ H4). rewrite Fmult2_correct. clear H4. intro H4. generalize (Fle2_correct _ _ H5). rewrite Fmult2_correct. clear H5. intro H5. apply IRmult_no with (1 := H1) (2 := H2) (3 := H3) (4 := H4) (5 := H5) (6 := Hx) (7 := Hy). Qed.
imports: Gappa_common Gappa_decimal