reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem Th42:
  0 <> n implies Sgm{n} = <* n *>
proof
  assume 0 <> n;
  then n in Seg n by FINSEQ_1:3;
  then {n} c= Seg n by ZFMISC_1:31;
  then
A3: {n} is included_in_Seg by FINSEQ_1:def 13;
  then len(Sgm{n}) = card{n} by Th37;
  then
A2: len(Sgm{n}) = 1 by CARD_1:30;
  rng(Sgm{n}) = {n} by A3,FINSEQ_1:def 14;
  hence thesis by A2,FINSEQ_1:39;
end;
