theorem
  for p,q being FinSequence, i being Nat st
  1 <= i & i <= len p holds (p ^ q).i = p.i
proof
  let p,q be FinSequence, i be Nat;
  assume
A1: 1 <= i & i <= len p;
  i in NAT & Seg len p = dom p by Def3,ORDINAL1:def 12;
  then i in dom p by A1;
  hence thesis by Def7;
end;
