reserve z,z1,z2 for Complex;
reserve r,x1,x2 for Real;
reserve p0,p,p1,p2,p3,q for Point of TOP-REAL 2;

theorem Th4:
  for p1,p2 st euc2cpx(p1)=euc2cpx(p2) holds p1=p2
proof
  let p1,p2;
  assume
A1: euc2cpx(p1)=euc2cpx(p2);
  p2 = cpx2euc(euc2cpx(p2)) by Th2;
  hence thesis by A1,Th2;
end;
