
theorem MaxEqMax:
  for f,g being Fuzzy_Negation,
      ff, gg being Membership_Func of [.0,1.] st
    f = ff & g = gg holds
    max(f,g) = max (ff,gg)
  proof
    let f,g being Fuzzy_Negation,
        ff, gg being Membership_Func of [.0,1.];
    assume
A1: f = ff & g = gg;
    consider f1,g1 being Function of [.0,1.], REAL such that
A2: f1 = f & g1 = g & max (f,g) = max (f1,g1) by MaxFuz;
    reconsider ff1 = f1, gg1 = g1 as Membership_Func of [.0,1.] by A2;
    for c being Element of [.0,1.] holds max(ff1,gg1).c = max(ff1.c,gg1.c)
      by FUZZY_1:def 4;
    hence thesis by A1,A2,COUSIN2:def 2;
  end;
