
theorem ConormProd:
  conorm prodnorm = probsum_conorm
  proof
    set dn = conorm prodnorm;
    set dc = probsum_conorm;
    for a,b being Element of [.0,1.] holds
      dc.(a,b) = 1 - (prodnorm).(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) = a + b - a*b by ProbSumDef
             .= 1 - (1-a) * (1-b)
             .= 1 - (prodnorm).(1-a,1-b) by ProdDef,A3;
      hence thesis;
    end;
    hence thesis by CoDef;
  end;
