let R be Relation; :: thesis: for X being set st R quasi_orders X holds
R ~ quasi_orders X
let X be set ; :: thesis: ( R quasi_orders X implies R ~ quasi_orders X )
assume ( R is_reflexive_in X & R is_transitive_in X ) ; :: according to ORDERS_1:def 6 :: thesis: R ~ quasi_orders X
hence ( R ~ is_reflexive_in X & R ~ is_transitive_in X ) by Lm11, Lm12; :: according to ORDERS_1:def 6 :: thesis: verum