theorem
  center G is commutative
proof
  let a,b be Element of center G;
  reconsider x = a, y = b as Element of G by GROUP_2:42;
A1: a in center G by STRUCT_0:def 5;
  thus a * b = x * y by GROUP_2:43
    .= y * x by A1,Th77
    .= b * a by GROUP_2:43;
end;
