proposition: Lemma In_mem {T : eqType} (x : T) l : reflect (In x l) (in_mem x (mem l)).
proof: Proof. apply iffP with (P := x \in l). by case: (x \in l) => // ; constructor. elim: l => [ | h l IH] //= E. rewrite in_cons in E. case/orP: E => E. now left ; apply sym_eq ; apply / eqP. right ; by apply IH. elim: l => [ | h l IH] E //=. simpl in E. case : E => E. rewrite E ; apply mem_head. rewrite in_cons. rewrite IH. apply orbT. by []. Qed.
imports: Coq(Reals Lia List ssreflect ssrbool) mathcomp(seq eqtype) Rcomplements