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;
