
theorem
  maxnorm = conorm minnorm
  proof
    for a,b being Element of [.0,1.] holds
      maxnorm.(a,b) = 1 - minnorm.(1 - a, 1 - b)
    proof
      let a,b be Element of [.0,1.];
A1:   1 - a in [.0,1.] & 1 - b in [.0,1.] by OpIn01;
      set e1 = -1;
A2:   - max(e1 * -a, e1 * -b) = - (e1 * min (-a,-b)) by MES57
         .= min (-a,-b);
A3:   min (1 +- a, 1 +- b) = 1 + min (-a, -b) by FUZZY_2:42
           .= 1 - max(a, b) by A2;
      maxnorm.(a,b) = 1 - min(1 - a, 1 - b) by A3,MaxDef
       .= 1 - minnorm.(1 - a, 1 - b) by A1,MinDef;
      hence thesis;
    end;
    hence thesis by CoDef;
  end;
