reserve x,y,z, X,Y,Z for set,
  n for Element of NAT;
reserve A for set,
  D for non empty set,
  a,b,c,l,r for Element of D,
  o,o9 for BinOp of D,
  f,g,h for Function of A,D;
reserve G for non empty multMagma;
reserve A for non empty set,
  a for Element of A,
  p for FinSequence of A,
  m1,m2 for Multiset of A;
reserve p,q for FinSequence of A;
reserve fm for Element of finite-MultiSet_over A;
reserve a,b,c for Element of D;

theorem Th44:
  for D1,D2,D being non empty set, f being Function of [:D1,D2:],D for
X1 being Subset of D1, X2 being Subset of D2 holds (f.:^2).(X1,X2) = f.:[:X1,X2
  :]
proof
  let D1,D2,D be non empty set, f be Function of [:D1,D2:],D;
  let X1 be Subset of D1, X2 be Subset of D2;
  [X1,X2]`1 = X1 & [X1,X2]`2 = X2;
  hence thesis by Def8;
end;
