proposition: Lemma set_ord_lt_prop3a a: ordinalp a -> ole_on a = ordinal_o a.
proof: Proof. move => oa. have [p2 p1]:= (wordering_ole_pr (Os_ordinal oa)). apply: sgraph_exten; try apply: order_is_graph; fprops. move => u v; split; move /graph_on_P1=> [pa pb pc]; apply /graph_on_P1 => //;split => //. + by case: pc. + split; [ exact:(Os_ordinal oa pa) | exact: (Os_ordinal oa pb) | done]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)