reserve V for RealLinearSpace;
reserve p,q,r,u,v,w,y,u1,v1,w1 for Element of V;
reserve a,b,c,d,a1,b1,c1,a2,b2,c2,a3,b3,e,f for Real;
reserve x,y,z for object;

theorem
  [x,y] in Proportionality_as_EqRel_of V implies x is Element of V & y
  is Element of V
proof
  assume [x,y] in Proportionality_as_EqRel_of V;
  then ex u,v st x=u & y=v & are_Prop u,v by Def3;
  then reconsider x,y as Element of V;
  x is Element of V & y is Element of V;
  hence thesis;
end;
