theorem
  |[ x1,x2,x3 ]| - |[ y1,y2,y3 ]| = (x1-y1)*<e1> + (x2-y2)*<e2> + (x3-y3)*<e3>
proof
A4: |[ x1,x2,x3 ]|.1 - |[ y1,y2,y3 ]|.1 = x1-y1;
A5: |[ x1,x2,x3 ]|.2 - |[ y1,y2,y3 ]|.2 = x2-y2;
 |[ x1,x2,x3 ]|.3 - |[ y1,y2,y3 ]|.3 = x3-y3;
    hence thesis by A4,A5,Th36;
end;
