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;

theorem
  L1 is Linear_Combination of A & L2 is Linear_Combination of A implies
  L1 - L2 is Linear_Combination of A
proof
  assume that
A1: L1 is Linear_Combination of A and
A2: L2 is Linear_Combination of A;
  - L2 is Linear_Combination of A by A2,Th44;
  hence thesis by A1,Th38;
end;
