proposition: Lemma add_test_constraint_left_false_lb : forall l1 u1 l2 u2 l u, add_test_constraint_left false (l1, u1) (l2, u2) = Some (l, u) -> l = l2.
proof: Proof. intros [l1 | | ] [u1 | | ] [l2 | | ] [u2 | | ] l u; unfold add_test_constraint_left; try (match goal with |- context[ext_eq ?a ?b] => case (ext_eq a b); intros Heq end); try (match goal with |- context[ext_eq ?a ?b] => case (ext_eq a b); intros Heq' end); try (simpl; intros; intuition; discriminate); try (intros H'; injection H'; intros; subst l; auto;fail). Qed.
imports: ZArith List Lia