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
  Carrier(L) = {v1,v2} & v1 <> v2 implies Sum(L) = L.v1 * v1 + L.v2 * v2
proof
  assume that
A1: Carrier(L) = {v1,v2} and
A2: v1 <> v2;
  L is Linear_Combination of {v1,v2} by A1,Def6;
  hence thesis by A2,Th33;
end;
