
theorem
  for t being t-conorm holds maxnorm <= t
  proof
    let t be t-conorm;
    set f1 = maxnorm;
    for a,b being Element of [.0,1.] holds
      f1.(a,b) <= t.(a,b)
    proof
      let a,b be Element of [.0,1.];
      reconsider aa = a, bb = b as Element of [.0,1.];
A1:   f1.(a,b) = max (aa,bb) by MaxDef;
      reconsider cc = 0 as Element of [.0,1.] by XXREAL_1:1;
      aa >= 0 by XXREAL_1:1; then
      t.(aa,bb) >= t.(cc,bb) by MonDef; then
      t.(aa,bb) >= t.(bb,cc) by BINOP_1:def 2; then
A3:   t.(aa,bb) >= bb by ZeroDef;
      bb >= 0 by XXREAL_1:1; then
      t.(aa,bb) >= t.(aa,cc) by MonDef; then
      t.(aa,bb) >= aa by ZeroDef;
      hence thesis by A1,XXREAL_0:28,A3;
    end;
    hence thesis;
  end;
