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 Th12:
  (-p)`1+(-p)`2*<i>= -(p`1)+(-(p`2))*<i>
proof
A1: -p=|[-p`1, -p`2]| by EUCLID:59;
  -(p`1)+(-(p`2))*<i> = -(p`1)+(-(p`2))*<i>;
  then
A2: Re(-(p`1)+-(p`2)*<i>)=-(p`1) & Im(-(p`1)+-(p`2)*<i>)=-(p`2) by COMPLEX1:12;
  Re((-p)`1+(-p)`2*<i>)=(-p)`1 by COMPLEX1:12;
  then Im((-p)`1+(-p)`2*<i>)=(-p)`2 & Re((-p)`1+(-p)`2*<i>)=-(p`1) by A1,
COMPLEX1:12,EUCLID:52;
  hence thesis by A1,A2,EUCLID:52;
end;
