theorem Th59:
  the carrier of H1 = the carrier of H2 implies
  the multMagma of H1 = the multMagma of H2
proof
  assume the carrier of H1 = the carrier of H2;
  then H1 is Subgroup of H2 & H2 is Subgroup of H1 by Th57;
  hence thesis by Th55;
end;
