{ i where i is Nat : i < len p } c= NAT

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in { i where i is Nat : i < len p } or x in NAT )
assume x in { i where i is Nat : i < len p } ; :: thesis: x in NAT
then ex i being Nat st
( i = x & i < len p ) ;
hence x in NAT by ORDINAL1:def 12; :: thesis: verum

end;

hence dom p is Subset of NAT by AXIOMS:4; :: thesis: verum