set f = I_GD ;
set g = I_FD ;
for x, y being Element of [.0,1.] holds I_GD . (x,y) <= I_FD . (x,y)

proof

let x, y be Element of [.0,1.]; :: thesis: I_GD . (x,y) <= I_FD . (x,y)

per cases ( x <= y or x > y ) ;

suppose A0: x <= y ; :: thesis: I_GD . (x,y) <= I_FD . (x,y)

then I_GD . (x,y) = 1 by FUZIMPL1:def 16;
hence I_GD . (x,y) <= I_FD . (x,y) by A0, FUZIMPL1:def 23; :: thesis: verum

end;

suppose A2: x > y ; :: thesis: I_GD . (x,y) <= I_FD . (x,y)

then A3: I_FD . (x,y) = max ((1 - x),y) by FUZIMPL1:def 23;
I_GD . (x,y) = y by A2, FUZIMPL1:def 16;
hence I_GD . (x,y) <= I_FD . (x,y) by A3, XXREAL_0:25; :: thesis: verum

end;

end;

end;

hence I_GD <= I_FD by FUZNORM1:def 16; :: thesis: verum