let R be Relation; :: thesis: for X being set st R partially_orders X holds
R ~ partially_orders X
let X be set ; :: thesis: ( R partially_orders X implies R ~ partially_orders X )
assume ( R is_reflexive_in X & R is_transitive_in X & R is_antisymmetric_in X ) ; :: according to ORDERS_1:def 7 :: thesis: R ~ partially_orders X
hence ( R ~ is_reflexive_in X & R ~ is_transitive_in X & R ~ is_antisymmetric_in X ) by Lm11, Lm12, Lm13; :: according to ORDERS_1:def 7 :: thesis: verum