let C be non empty set ; :: thesis: for f, g being Membership_Func of C holds
( f c= & max f,g c= )
let f, g be Membership_Func of C; :: thesis: ( f c= & max f,g c= )
thus f c= :: thesis: max f,g c=

proof

let x be Element of C; :: according to FUZZY_1:def 3 :: thesis: (min f,g) . x <= f . x
(min f,g) . x = min (f . x),(g . x) by Def4;
hence (min f,g) . x <= f . x by XXREAL_0:17; :: thesis: verum

end;

let x be Element of C; :: according to FUZZY_1:def 3 :: thesis: f . x <= (max f,g) . x
(max f,g) . x = max (f . x),(g . x) by Def5;
hence f . x <= (max f,g) . x by XXREAL_0:25; :: thesis: verum