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;

theorem
  L1 is C_Linear_Combination of A & L2 is C_Linear_Combination of A
  implies L1 - L2 is C_Linear_Combination of A
proof
  assume that
A1: L1 is C_Linear_Combination of A and
A2: L2 is C_Linear_Combination of A;
  - L2 is C_Linear_Combination of A by A2,Th26;
  hence thesis by A1,Th20;
end;
