let R be Relation; :: thesis: for X being set st R is being_linear-order holds
R |_2 X is being_linear-order
let X be set ; :: thesis: ( R is being_linear-order implies R |_2 X is being_linear-order )
assume ( R is reflexive & R is transitive & R is antisymmetric & R is connected ) ; :: according to ORDERS_1:def 5 :: thesis: R |_2 X is being_linear-order
hence ( R |_2 X is reflexive & R |_2 X is transitive & R |_2 X is antisymmetric & R |_2 X is connected ) by WELLORD1:22, WELLORD1:23, WELLORD1:24, WELLORD1:25; :: according to ORDERS_1:def 5 :: thesis: verum