theorem
  v1 <> v2 implies Sum{v1,v2} = v1 + v2
proof
  assume v1 <> v2;
  then
A1: <* v1,v2 *> is one-to-one by FINSEQ_3:94;
  rng<* v1,v2 *> = {v1,v2} & Sum<* v1,v2 *> = v1 + v2 by FINSEQ_2:127
,RLVECT_1:45;
  hence thesis by A1,Def1;
end;
