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;
