let X, Y be non empty TopSpace; :: thesis: for a, b being Element of (oContMaps X,Y)
for f, g being Function of X,(Omega Y) st a = f & b = g holds
( a <= b iff f <= g )
let a, b be Element of (oContMaps X,Y); :: thesis: for f, g being Function of X,(Omega Y) st a = f & b = g holds
( a <= b iff f <= g )
let f, g be Function of X,(Omega Y); :: thesis: ( a = f & b = g implies ( a <= b iff f <= g ) )
assume A1: ( a = f & b = g ) ; :: thesis: ( a <= b iff f <= g )
A2: oContMaps X,Y is full SubRelStr of (Omega Y) |^ the carrier of X by WAYBEL24:def 3;
then reconsider x = a, y = b as Element of ((Omega Y) |^ the carrier of X) by YELLOW_0:59;
( a <= b iff x <= y ) by A2, YELLOW_0:60, YELLOW_0:61;
hence ( a <= b iff f <= g ) by A1, WAYBEL10:12; :: thesis: verum