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 Th10:
  |[Re (-z),Im (-z)]|=|[-(Re z), -(Im z)]|
proof
  (|[Re (-z),Im (-z)]|)`2=Im (-z) by EUCLID:52;
  then
A1: (|[Re (-z),Im (-z)]|)`2=-(Im z) by COMPLEX1:17;
  (|[Re (-z),Im (-z)]|)`1=Re (-z) by EUCLID:52;
  then (|[Re (-z),Im (-z)]|)`1=-(Re z) by COMPLEX1:17;
  hence thesis by A1,EUCLID:53;
end;
