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 Th13:
  |[x1, y1, z1]| - |[x2, y2, z2]| = |[ x1-x2, y1-y2, z1-z2]|
proof
A1: |[x1, y1, z1]|`3 = z1 & |[x2, y2, z2]|`1 = x2;
A2: |[x2, y2, z2]|`2 = y2 & |[x2, y2, z2]|`3 = z2;
  |[x1, y1, z1]|`1 = x1 & |[x1, y1, z1]|`2 = y1;
  hence thesis by A1,A2,Th12;
end;
