proposition: Lemma not_0_ltb : forall x, x <> 0 <-> 0 <? x = true.
proof: Proof. intros x;rewrite ltb_spec, to_Z_0;assert (W:=to_Z_bounded x);split. intros Hd;assert ([|x|] <> 0)%Z;[ | lia]. intros Heq;elim Hd;apply to_Z_inj;trivial. intros Hlt Heq;elimtype False. assert ([|x|] = 0)%Z;[ rewrite Heq, to_Z_0;trivial | lia]. Qed.
imports: Bool List PArray Int63 Ring63 ZArith Psatz