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
  -|[x1,y1,z1]| = |[ -x1, -y1, -z1]|
proof
A1: |[x1,y1,z1]|`3 = z1;
  |[x1,y1,z1]|`1 = x1 & |[x1,y1,z1]|`2 = y1;
  hence thesis by A1,Th10;
end;
