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 Th46:
  Sgm Seg k = idseq k
proof
  defpred P[Nat] means Sgm Seg $1 = idseq $1;
A1: for k being Nat st P[k] holds P[k+1] by Lm5;
A2: P[0] by Th41;
  for k being Nat holds P[k] from NAT_1:sch 2(A2,A1);
  hence thesis;
end;
