Record primestream :=
  {
    str :> nat -> nat;
    str_inj : forall n m, str n = str m -> n = m;
    str_prime : forall n, prime (str n);
  }.Record primestream :=
  {
    str :> nat -> nat;
    str_inj : forall n m, str n = str m -> n = m;
    str_prime : forall n, prime (str n);
  }.Record primestream :=
  {
    str :> nat -> nat;
    str_inj : forall n m, str n = str m -> n = m;
    str_prime : forall n, prime (str n);
  }.Record primestream :=
  {
    str :> nat -> nat;
    str_inj : forall n m, str n = str m -> n = m;
    str_prime : forall n, prime (str n);
  }.

Lemma primestream_divides (ps : primestream) n m : divides (ps n) (ps m) -> n = m.