theorem nle_inv_succ_1: \forall x,y. x < y \to
\exists z. y = succ z \land x <= z.
- intros. inversion H; clear H; intros; subst. auto.
+ intros. inversion H; clear H; intros; subst. autobatch.
qed.
theorem nle_inv_succ_succ: \forall x,y. x < succ y \to x <= y.
- intros. inversion H; clear H; intros; subst. auto.
+ intros. inversion H; clear H; intros; subst. autobatch.
qed.
theorem nle_inv_succ_zero: \forall x. x < zero \to False.
qed.
theorem nle_inv_zero_2: \forall x. x <= zero \to x = zero.
- intros. inversion H; clear H; intros; subst. auto.
+ intros. inversion H; clear H; intros; subst. autobatch.
qed.
theorem nle_inv_succ_2: \forall y,x. x <= succ y \to