proposition: Lemma limit_unique : forall x l1 l2, IsLimit x l1 -> IsLimit x l2 -> l1 = l2.
proof: Proof. intros x l1 l2 E1 E2. apply separated. intros e. rewrite (pos_split2 e),(pos_split2 (e/2)). apply triangular with (x (e / 2 / 2));[symmetry;apply E1|apply E2]. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.rationals HoTT.Classes.interfaces.orders HoTT.Classes.implementations.peano_naturals HoTT.Classes.implementations.natpair_integers HoTT.Classes.theory.groups HoTT.Classes.theory.integers HoTT.Classes.theory.dec_fields HoTT.Classes.orders.dec_fields HoTT.Classes.orders.sum HoTT.Classes.theory.rationals HoTT.Classes.orders.lattices HoTT.Classes.implementations.assume_rationals HoTT.Classes.tactics.ring_quote HoTT.Classes.tactics.ring_tac