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 Th17:
  for U0 be with_const_op Universal_Algebra,U1,U2 be SubAlgebra of
  U0 holds the carrier of U1 meets the carrier of U2
proof
  let U0 be with_const_op Universal_Algebra, U1,U2 be SubAlgebra of U0;
  set a = the Element of Constants(U0);
  Constants(U0) is non empty Subset of U1 & Constants(U0) is non empty
  Subset of U2 by Th15;
  then
A1: Constants(U0) c= (the carrier of U1) /\ (the carrier of U2) by XBOOLE_1:19;
  thus thesis by A1;
end;
