Open Scope Z_scope.
(* Pierre L: examples gathered while debugging romega. *)
(* Starting from Coq 8.9 (late 2018), `romega` tactics are deprecated. The tests in this file remain but now call the `lia` tactic. *)

Lemma test_lia_3 : forall a b h hl hr ha hb,
0 <= ha - hl <= 1 ->
-2 <= hl - hr <= 2 ->
h =b+1 ->
(ha >= hr /\ a = ha \/ ha <= hr /\ a = hr) ->
(hl >= hr /\ b = hl \/ hl <= hr /\ b = hr) ->
(-3 <= ha -hr <=3 -> 0 <= hb - a <= 1) ->
(-2 <= ha-hr <=2 -> hb = a  + 1) ->
0 <= hb - h <= 1.