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,Def4;
  hence thesis by A2,Th18;
end;
