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

theorem Th20:
  for q being FinSubsequence holds ex p being FinSequence st q c= p
proof
  let q be FinSubsequence;
  consider k being Nat such that
A1: dom q c= Seg k by FINSEQ_1:def 12;
  reconsider IK = id Seg k as Function;
  set IS = IK +* q;
  dom IS = dom IK \/ dom q by FUNCT_4:def 1
    .= Seg k \/ dom q
    .= Seg k by A1,XBOOLE_1:12;
  then reconsider IS as FinSequence by FINSEQ_1:def 2;
  q c= IS by FUNCT_4:25;
  hence thesis;
end;
