let R be Relation; :: thesis: for X being set st R is being_quasi-order holds
R |_2 X is being_quasi-order
let X be set ; :: thesis: ( R is being_quasi-order implies R |_2 X is being_quasi-order )
assume that
A1: R is reflexive and
A2: R is transitive ; :: according to ORDERS_1:def 3 :: thesis: R |_2 X is being_quasi-order
thus ( R |_2 X is reflexive & R |_2 X is transitive ) by A1, A2, WELLORD1:15, WELLORD1:17; :: according to ORDERS_1:def 3 :: thesis: verum