reserve r,s,t,u for Real;
reserve V for RealLinearSpace,
  v,w for Point of V;
reserve x1,x2,x3,x4,y1,y2 for Element of V;

theorem
 for x being object st x in LSeg(v,w)
 ex r st 0<=r & r<=1 & x=(1-r)*v+r*w
 proof let x be object;
  assume x in LSeg(v,w);
   then ex r st x = (1-r)*v + r*w & 0 <= r & r <= 1;
  hence ex r st 0<=r & r<=1 & x=(1-r)*v+r*w;
 end;
