proposition: Lemma pop2_bop2 : forall (op : Op2) (r1 r2 : R), is_true (Reval_bop2 op r1 r2) <-> Reval_pop2 op r1 r2.
proof: Proof. unfold is_true. destruct op ; simpl; intros; match goal with | |- context[sumboolb (?F ?X ?Y)] => destruct (F X Y) ; simpl; intuition try congruence end. - apply Rlt_not_le in r. tauto. - apply Rgt_not_ge in r. tauto. - apply Rlt_not_le in H. tauto. Qed.
imports: OrderedRing QMicromega RingMicromega Refl Sumbool Raxioms Rfunctions RIneq Rpow_def QArith Qfield Qreals DeclConstant EnvRing