reserve n for Nat,
  a, b, r, w for Real,
  x, y, z for Point of TOP-REAL n,
  e for Point of Euclid n;
reserve V for RealLinearSpace,
        p,q,x for Element of V;

theorem
  LSeg(p,q) c= halfline(p,q)
proof
  let a be object;
  assume a in LSeg(p,q);
  then ex r being Real st 0<=r & r<=1 & a = (1-r)*p+r*q by RLTOPSP1:76;
  hence thesis;
end;
