reserve U0,U1,U2,U3 for Universal_Algebra,
  n for Nat,
  x,y for set;
reserve A for non empty Subset of U0,
  o for operation of U0,
  x1,y1 for FinSequence of A;

theorem Th21:
  for U0 be Universal_Algebra, U1,U2 be SubAlgebra of U0 holds U1
  "\/" U2 = U2 "\/" U1
proof
  let U0 be Universal_Algebra ,U1,U2 be SubAlgebra of U0;
  reconsider u1=the carrier of U1,u2=the carrier of U2 as non empty Subset of
  U0 by Def7;
  reconsider A = u1 \/ u2 as non empty Subset of U0;
  U1 "\/" U2 = GenUnivAlg(A) by Def13;
  hence thesis by Def13;
end;
