reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;
reserve i,j for Nat;
reserve F for Function,
  e,x,y,z for object;
reserve a,b,c for set;

theorem
  for A, B being non empty set, f being Function of A, B, x being
  Element of A, y being set holds f+*(x,y).x = y
proof
  let A, B be non empty set, f be Function of A, B, x be Element of A, y be
  set;
  x in A;
  then x in dom f by FUNCT_2:def 1;
  hence thesis by Th30;
end;
