reserve x,y for set,
  i for Nat;
reserve V for non empty CLSStruct,
  u,v,v1,v2,v3 for VECTOR of V,
  A for Subset of V,
  l, l1, l2 for C_Linear_Combination of A,
  x,y,y1,y2 for set,
  a,b for Complex,
  F for FinSequence of the carrier of V,
  f for Function of the carrier of V, COMPLEX;
reserve K,L,L1,L2,L3 for C_Linear_Combination of V;
reserve e,e1,e2 for Element of C_LinComb V;

theorem
  vector(LC_CLSpace V,L1) - vector(LC_CLSpace V,L2) = L1 - L2
proof
  - L2 in C_LinComb V by Def12;
  then
A1: - L2 in LC_CLSpace V;
  - vector(LC_CLSpace V,L2) = - L2 by Th40
    .= vector(LC_CLSpace V,- L2) by A1,RLVECT_2:def 1;
  hence thesis by Th38;
end;
