proposition: Lemma path_supp_ins_inv k1 k v (s : fmap) : path ord k (supp s) -> path ord k1 (supp (ins k v s)) -> ord k1 k && path ord k1 (supp s).
proof: Proof. case: s=>s p; rewrite /supp /= => H1; rewrite last_ins' //=. by case/andP=>H2 H3; rewrite H2; apply: ord_path H3. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path) pcm(options)