set A = [.0,1.];
deffunc H1( Element of [.0,1.], Element of [.0,1.]) -> Element of [.0,1.] = In ((max ($2,(min ((1 - $1),(1 - $2))))),[.0,1.]);
ex f being Function of [:[.0,1.],[.0,1.]:],[.0,1.] st
for x, y being Element of [.0,1.] holds f . (x,y) = H1(x,y)
from BINOP_1:sch 4();
then consider f being BinOp of [.0,1.] such that
A1:
for x, y being Element of [.0,1.] holds f . (x,y) = H1(x,y)
;
take
f
; for x, y being Element of [.0,1.] holds f . (x,y) = max (y,(min ((1 - x),(1 - y))))
let a, b be Element of [.0,1.]; f . (a,b) = max (b,(min ((1 - a),(1 - b))))
f . (a,b) = H1(a,b)
by A1;
hence
f . (a,b) = max (b,(min ((1 - a),(1 - b))))
by SUBSET_1:def 8, MaxMinIn01; verum