
theorem ConormLukasiewicz:
  conorm Lukasiewicz_norm = BoundedSum_conorm
  proof
    set dn = conorm Lukasiewicz_norm;
    set dc = BoundedSum_conorm;
    for a,b being Element of [.0,1.] holds
      dc.(a,b) = 1 - (Lukasiewicz_norm).(1-a,1-b)
    proof
      let a,b be Element of [.0,1.];
A3:   1 - a in [.0,1.] & 1 - b in [.0,1.] by OpIn01;
      dc.(a,b) = min (a+b,1) by LukConorm
             .= 1 - max (0,1-a+(1-b)-1) by LukasiDual
             .= 1 - (Lukasiewicz_norm).(1-a,1-b) by LukNorm,A3;
      hence thesis;
    end;
    hence thesis by CoDef;
  end;
