reserve n, k, r, m, i, j for Nat;

theorem Th17:
  for k being Element of NAT, a being set st k >= 1 holds {[k, a]}
  is FinSubsequence
proof
  let k be Element of NAT, a be set;
  reconsider H = {[k,a]} as Function;
A1: dom H = {k} by RELAT_1:9;
  assume
A2: k >= 1;
  dom H c= Seg k
  proof
    let x be object;
    assume x in dom H;
    then x = k by A1,TARSKI:def 1;
    hence thesis by A2;
  end;
  hence thesis by FINSEQ_1:def 12;
end;
