proposition: Lemma Interval_restrict_pr : forall a b E x (E': a <= x /\ x <= b), Interval_restrict a b E x = exist _ x E'.
proof: Proof. intros a b E x E'. unfold Interval_restrict. apply Sigma.path_sigma_hprop. simpl. rewrite meet_l;[apply join_r|];apply E'. 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