reserve a, b, c, d, e for Complex;

theorem Th211:
  a <> 0 & b <> 0 implies a" + b" = (a + b)*(a*b)"
proof
  assume that
A1: a <> 0 and
A2: b <> 0;
  b" = b"*1;
  then b" = b"*(a"*a) by A1,XCMPLX_0:def 7;
  then b" = (a"*b")*a;
  then
A3: b" = (a*b)"*a by Lm1;
  a" = a"*1;
  then a" = a"*(b"*b) by A2,XCMPLX_0:def 7;
  then a" = (a"*b")*b;
  then a" = (a*b)"*b by Lm1;
  hence thesis by A3;
end;
