proposition: Lemma path_mem_irr (s : seq A) ltT x : irreflexive ltT -> transitive ltT -> path ltT x s -> x \notin s.
proof: Proof. move=>I T P; apply: contraFT (I x). by rewrite negbK; apply: path_mem T P. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat seq path eqtype choice bigop) pcm(options prelude pred)