let x, y be Surreal; for X being set holds comp (X,x,y,{}) = {}
let X be set ; comp (X,x,y,{}) = {}
assume
comp (X,x,y,{}) <> {}
; contradiction
then consider o being object such that
A1:
o in comp (X,x,y,{})
by XBOOLE_0:def 1;
consider x1, y1 being Surreal such that
A2:
( o = ((x1 * y) +' (x * y1)) +' (-' (x1 * y1)) & x1 in X & y1 in {} )
by A1, Def14;
thus
contradiction
by A2; verum