reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem
  a+b*<i> = c+d*<i> implies a = c & b = d
proof
  assume
A1: a+b*<i> = c+d*<i>;
  then a-c+(b-d)*<i> = 0;
  then a-c = 0 by Th4,Th12;
  hence thesis by A1;
end;
