theorem
  for p being FinSequence, k being Nat st k in dom p
  for i being Nat st 1 <= i & i <= k holds i in dom p
proof
  let p be FinSequence, k be Nat;
  assume
A1: k in dom p;
  let i be Nat;
  assume that
A2: 1 <= i and
A3: i <= k;
  k <= len p by A1,Th25;
  then i <= len p by A3,XXREAL_0:2;
  hence thesis by A2,Th25;
end;
