let R be Relation; :: thesis: ( R is being_linear-order implies ( R is being_quasi-order & R is being_partial-order ) )
assume that
A1: R is reflexive and
A2: R is transitive and
A3: R is antisymmetric and
R is connected ; :: according to ORDERS_1:def 5 :: thesis: ( R is being_quasi-order & R is being_partial-order )
thus ( R is reflexive & R is transitive & R is reflexive & R is transitive & R is antisymmetric ) by A1, A2, A3; :: according to ORDERS_1:def 3,ORDERS_1:def 4 :: thesis: verum