reserve a,b,r for non unit non zero Real;
reserve X for non empty set,
        x for Tuple of 4,X;
reserve V             for RealLinearSpace,
        A,B,C,P,Q,R,S for Element of V;

theorem Th17:
  for T being RealLinearSpace
  for x being Element of T
  for p being Element of TOP-REAL 1 st
  T = TOP-REAL 1 & p = x
  holds - p = - x
  proof
    let T be RealLinearSpace;
    let x be Element of T;
    let p be Element of TOP-REAL 1;
    assume that
A1: T = TOP-REAL 1 and
A2: p = x;
    p is Element of REAL 1 by EUCLID:22;
    then reconsider p9 = p as Tuple of 1,REAL;
    - p9 = - x by A1,A2,Th16;
    hence thesis;
  end;
