proposition: Lemma non_collectivizing_ordinal: non_coll ordinalp.
proof: Proof. move=> [x xp]. have osx: ordinal_set x by move => t /xp. have yo: ordinalp x. by apply: ordinal_pr => // a ay b ba; move/xp: (Os_ordinal (osx _ ay) ba). by case:(ordinal_irreflexive yo); apply/xp. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)