Answer by Link L for How to to use the fact that combining these hypothesis is false in Coq

whatever .. here's a long-cut...

Lemma helper : forall a y, a > y -> a <= y -> False.Proof.    intros. destruct y.    - destruct a.+ apply Arith_prebase.gt_irrefl_stt in H. destruct H.+ apply Arith_prebase.le_n_0_eq_stt in H0.            rewrite H0 in H. apply Arith_prebase.gt_irrefl_stt in H. destruct H.    - destruct a.+ apply Arith_prebase.gt_not_le_stt in H. unfold not in H.            apply H in H0. destruct H0.+ apply Arith_prebase.gt_not_le_stt in H. unfold not in H.            apply H in H0. destruct H0.Qed.