proposition: Theorem intersect_bh : forall z : R, forall yf : float2, forall xi zi : FF, BND z xi -> (yf <= z)%R -> intersect_helper (upper xi) yf zi = true -> BND z zi.
proof: Proof. intros z yf xi zi Hx Hy Hb. generalize (andb_prop _ _ Hb). clear Hb. intros (H1,H2). generalize (Fle2_correct _ _ H1). clear H1. intro H1. generalize (Fle2_correct _ _ H2). clear H2. intro H2. split. apply Rle_trans with (1 := H1) (2 := Hy). apply Rle_trans with (1 := (proj2 Hx)) (2 := H2). Qed.
imports: Gappa_common Gappa_decimal