-interpretation "cons (nstream)" 'Cons b t = (seq ? b t).
-
-coinductive eq_stream (A): relation (stream A) ≝
-| eq_sec: ∀t1,t2,b1,b2. b1 = b2 → eq_stream A t1 t2 → eq_stream A (b1@t1) (b2@t2)
-.
-
-interpretation "extensional equivalence (nstream)"
- 'ExtEq A t1 t2 = (eq_stream A t1 t2).
-
-definition eq_stream_repl_back (A) (R:predicate …) (t1,t2) ≝
- t1 ≐⦋A⦌ t2 → R t1 → R t2.
-
-definition eq_stream_repl_fwd (A) (R:predicate …) (t1,t2) ≝
- t2 ≐⦋A⦌ t1 → R t1 → R t2.
-
-(* Basic inversion lemmas ***************************************************)
-
-fact eq_stream_inv_seq_aux: ∀A,t1,t2. t1 ≐⦋A⦌ t2 →
- ∀u1,u2,a1,a2. t1 = a1@u1 → t2 = a2@u2 →
- a1 = a2 ∧ u1 ≐ u2.
-#A #t1 #t2 * -t1 -t2
-#t1 #t2 #b1 #b2 #Hb #Ht #u1 #u2 #a1 #a2 #H1 #H2 destruct /2 width=1 by conj/
-qed-.
-
-lemma eq_stream_inv_seq: ∀A,t1,t2,b1,b2. b1@t1 ≐⦋A⦌ b2@t2 → b1 = b2 ∧ t1 ≐ t2.
-/2 width=5 by eq_stream_inv_seq_aux/ qed-.