proposition: Theorem nzr_of_abs : forall z : R, forall zi : FF, ABS z zi -> Fpos (lower zi) = true -> NZR z.
proof: Proof. intros z zi Hz Hb. generalize (Fpos_correct _ Hb). clear Hb. intro H. case (Rcase_abs z) ; intro. apply Rlt_not_eq with (1 := r). rewrite <- (Rabs_right z r). unfold NZR. apply Rgt_not_eq. apply Rlt_le_trans with (1 := H) (2 := proj1 (proj2 Hz)). Qed.
imports: Gappa_common