reserve V, C for set;
reserve A, B, D for Element of Fin PFuncs (V, C);
reserve s for Element of PFuncs (V,C);

theorem Th14:
  A c= B implies A ^ D c= B ^ D
proof
  deffunc U(Element of PFuncs (V,C),Element of PFuncs (V,C)) = $1 \/ $2;
  defpred X[Function,Function] means $1 in A & $2 in D & $1 tolerates $2;
  defpred Y[Function,Function] means $1 in B & $2 in D & $1 tolerates $2;
  set X1 = { U(s,t) where s, t is Element of PFuncs (V,C) : X[s,t]}, X2 = { U(
  s,t) where s, t is Element of PFuncs (V,C) : Y[s,t]};
  assume A c= B;
  then
A1: for s, t being Element of PFuncs (V,C) holds X[s,t] implies Y[s,t];
  X1 c= X2 from FRAENKEL:sch 2(A1);
  hence thesis;
end;
