proposition: Lemma order_from_rel r x: order_r r -> order (graph_on r x).
proof: Proof. move=> [ta tb tc]. have [tr pa pb]: preorder (graph_on r x) by apply: preorder_from_rel; split. split => //. by move=> a b /graph_on_P1 [ax bx rab] /graph_on_P1 [_ _ rba]; apply: tb. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)