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
  (x*p)`1 = x * p`1 & (x*p)`2 = x * p`2 & (x*p)`3 = x * p`3
proof
A1: (x*p)`3 = |[ x*p`1 ,x*p`2 ,x*p`3]|`3 by Th7;
  (x*p)`1 = |[ x*p`1 ,x*p`2 ,x*p`3]|`1 & (x*p)`2 = |[ x*p`1 ,x*p`2 ,x*p`3
  ]|`2 by Th7;
  hence thesis by A1;
end;
