
theorem
  for N1,N2 being Element of Fuzzy_Negations,
      NN1,NN2 being Fuzzy_Negation st N1 = NN1 & N2 = NN2 holds
    N1 "/\" N2 = min (NN1,NN2)
  proof
    let N1,N2 be Element of Fuzzy_Negations,
        NN1,NN2 be Fuzzy_Negation;
    assume
A0: N1 = NN1 & N2 = NN2;
    reconsider s = N1, t = N2 as Element of FuzzyLattice [.0,1.]
      by YELLOW_0:58;
A4: s "/\" t = N1 "/\" N2 by YELLOW_0:69;
    s "/\" t = min(@s, @t) by LFUZZY_0:21;
    hence thesis by A0,A4,MinEqMin;
  end;
