reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;
reserve a, b, c, d, e, f for object;

theorem
  i > 0 implies {[i,x]} is FinSubsequence
proof
  assume
A1: i > 0;
A2: dom {[i,x]} = {i} by RELAT_1:9;
  {i} c= Seg i
  proof
    let x be object;
    assume x in {i};
    then x = i by TARSKI:def 1;
    hence thesis by A1,Th3;
  end;
  hence thesis by A2,Def12;
end;
