reserve x,y,y1,y2 for set,
  p for FinSequence,
  i,k,l,n for Nat,
  V for RealLinearSpace,
  u,v,v1,v2,v3,w for VECTOR of V,
  a,b for Real,
  F,G,H1,H2 for FinSequence of V,
  A,B for Subset of V,
  f for Function of the carrier of V, REAL;
reserve K,L,L1,L2,L3 for Linear_Combination of V;
reserve l,l1,l2 for Linear_Combination of A;
reserve e,e1,e2 for Element of LinComb(V);

theorem
  vector(LC_RLSpace(V),L1) - vector(LC_RLSpace(V),L2) = L1 - L2
proof
  - L2 in LinComb(V) by Def14;
  then
A1: - L2 in LC_RLSpace(V);
  - vector(LC_RLSpace(V),L2) = - L2 by Th64
    .= vector(LC_RLSpace(V),- L2) by A1,Def1;
  hence thesis by Th62;
end;
