theorem
  H1 is finite or H2 is finite implies H1 /\ H2 is finite
proof
  assume
A1: H1 is finite or H2 is finite;
  H1 /\ H2 is Subgroup of H1 & H1 /\ H2 is Subgroup of H2 by Lm4;
  hence thesis by A1;
end;
