reserve V for RealLinearSpace;
reserve p,q,u,v,w,y for VECTOR of V;
reserve a,b,c,d for Real;

theorem Th15:
  v-u=y-w implies u,v // w,y
proof
  assume v-u=y-w;
  then jj*(v-u)=jj*(y-w);
  hence thesis;
end;
