reserve x,O for set,
  o for Element of O,
  G,H,I for GroupWithOperators of O,
  A, B for Subset of G,
  N for normal StableSubgroup of G,
  H1,H2,H3 for StableSubgroup of G,
  g1,g2 for Element of G,
  h1,h2 for Element of H1,
  h for Homomorphism of G,H;

theorem Th20:
  H1 /\ H2 /\ H3 = H1 /\ (H2 /\ H3)
proof
  the carrier of H1 /\ H2 /\ H3 = carr(H1 /\ H2) /\ carr(H3) by Def25
    .= carr(H1) /\ carr(H2) /\ carr(H3) by Def25
    .= carr(H1) /\ (carr(H2) /\ carr(H3)) by XBOOLE_1:16
    .= carr(H1) /\ carr(H2 /\ H3) by Def25
    .= the carrier of H1 /\ (H2 /\ H3) by Def25;
  hence thesis by Lm4;
end;
