theorem Th20:
  min(f,g) = (C,f)@ "/\" (C,g)@
proof
  set fg = (C,f)@ "/\" (C,g)@, R = RealPoset [. 0,1 .], J = C --> R;
A1: (RealPoset [. 0,1 .]) |^ C = product (C --> RealPoset [. 0,1 .]) by
YELLOW_1:def 5;
  now
    let c;
    ( for c being Element of C holds J.c is Semilattice)& J.c = RealPoset
    [. 0,1 .];
    hence (@fg).c = ((C,f)@.c) "/\" ((C,g)@.c) by A1,Th11
      .= min(f.c, g.c);
  end;
  hence thesis by FUZZY_1:def 3;
end;
