reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem
  1 <= n & f is non empty implies (Ins(f,n,p)).1 = f.1
proof
  assume that
A1: 1 <= n and
A2: f is non empty;
A3: n <= len f implies len(f|n) = n by FINSEQ_1:59;
  1 <= len f by A2,NAT_1:14;
  then 1 <= len(f|n) by A1,A3,FINSEQ_1:58;
  then 1 in dom(f|n) by FINSEQ_3:25;
  hence thesis by Th72;
end;
