reserve r,s,t,u for Real;
reserve V for RealLinearSpace,
  v,w for Point of V;

theorem :: TOPREAL1:7
  LSeg(v,v) = {v}
proof
  thus LSeg(v,v) c= {v}
  proof
    let a be object;
    assume a in LSeg(v,v);
    then consider r such that
A1: a = (1-r)*v + r*v and
    0 <= r and
    r <= 1;
    a = ((1-r)+r)*v by A1,RLVECT_1:def 6
      .= v by RLVECT_1:def 8;
    hence thesis by TARSKI:def 1;
  end;
  v in LSeg(v,v) by Th68;
  hence thesis by ZFMISC_1:31;
end;
