reserve x,y,z for Real,
  x3,y3 for Real,
  p for Point of TOP-REAL 3;
reserve p1,p2,p3,p4 for Point of TOP-REAL 3,
  x1,x2,y1,y2,z1,z2 for Real;

theorem Th24:
  (p1+p2) <X> p3 = ( p1 <X> p3 ) + ( p2 <X> p3 )
proof
  (p1+p2) <X> p3 = - ( p3 <X> (p1+p2) ) by Th17
    .= - ( ( p3 <X> p1 ) + ( p3 <X> p2 ) ) by Th23
    .= - ( ( p3 <X> p1 ) - ( p2 <X> p3 ) ) by Th17
    .= - ( p3 <X> p1 ) + ( p2 <X> p3 ) by RLVECT_1:33;
  hence thesis by Th17;
end;
