(* STREAMS ******************************************************************)
coinductive eq_stream (A): relation (stream A) ≝
-| eq_seq: ∀t1,t2,b1,b2. b1 = b2 → eq_stream A t1 t2 → eq_stream A (b1@t1) (b2@t2)
+| eq_seq: ∀t1,t2,b1,b2. b1 = b2 → eq_stream A t1 t2 → eq_stream A (b1⨮t1) (b2⨮t2)
.
interpretation "extensional equivalence (nstream)"
(* Basic inversion lemmas ***************************************************)
lemma eq_stream_inv_seq: ∀A,t1,t2. t1 ≗{A} t2 →
- ∀u1,u2,a1,a2. a1@u1 = t1 → a2@u2 = t2 →
+ ∀u1,u2,a1,a2. a1⨮u1 = t1 → a2⨮u2 = t2 →
u1 ≗ u2 ∧ a1 = a2.
#A #t1 #t2 * -t1 -t2
#t1 #t2 #b1 #b2 #Hb #Ht #u1 #u2 #a1 #a2 #H1 #H2 destruct /2 width=1 by conj/