-lemma dfr_lift_bi (f) (p) (q) (t1) (t2): t1 ϵ 𝐓 →
- t1 ➡𝐝𝐟[p,q] t2 → ↑[f]t1 ➡𝐟[⊗p,⊗q] ↑[f]t2.
-#f #p #q #t1 #t2 #H0t1
-* #b #n * #Hb #Hn #Ht1 #Ht2
-@(ex1_2_intro … (⊗b) (↑❘⊗q❘)) @and4_intro
+(* COMMENT
+axiom pippo (b) (q) (n):
+ ↑❘q❘ = (↑[q]𝐢)@❨n❩ →
+ ↑❘q❘+❘b❘= (↑[b●𝗟◗q]𝐢)@❨n+❘b❘❩.
+
+lemma unwind_rmap_tls_eq_id (p) (n):
+ ❘p❘ = ↑[p]𝐢@❨n❩ →
+ (𝐢) ≗ ⇂*[n]↑[p]𝐢.
+#p @(list_ind_rcons … p) -p
+[ #n <depth_empty #H destruct
+| #p * [ #m ] #IH #n
+ [ <depth_d_dx <unwind_rmap_pap_d_dx #H0
+ @(stream_eq_trans … (unwind_rmap_tls_d_dx …))
+ @(stream_eq_trans … (IH …)) -IH //
+ | /2 width=1 by/
+ | <depth_L_dx <unwind_rmap_L_dx
+ cases n -n [| #n ] #H0
+ [
+ |
+ ]
+ | /2 width=1 by/
+ | /2 width=1 by/
+ ]
+]
+
+
+(* (↑❘q❘+❘b❘=↑[b●𝗟◗q]𝐢@❨n+❘b❘❩ *)
+(* [↑[p]𝐢@❨n❩]⫯*[❘p❘]f∘⇂*[n]↑[p]𝐢) *)
+lemma unwind_rmap_tls_eq (f) (p) (n):
+ ❘p❘ = ↑[p]𝐢@❨n❩ →
+ f ≗ ⇂*[n]↑[p]f.
+#f #p #n #Hp
+@(stream_eq_canc_dx … (stream_tls_eq_repl …))
+[| @unwind_rmap_decompose | skip ]
+<tr_compose_tls <Hp
+
+@(stream_eq_canc_dx) … (unwind_rmap_decompose …))
+
+*)
+lemma dfr_unwind_id_bi (p) (q) (t1) (t2): t1 ϵ 𝐓 →
+ t1 ➡𝐝𝐟[p,q] t2 → ▼[𝐢]t1 ➡𝐟[⊗p,⊗q] ▼[𝐢]t2.
+#p #q #t1 #t2 #H0t1
+* #b #n * #Hb #Hn #Ht1 #Ht2
+@(ex1_2_intro … (⊗b) (↑♭⊗q)) @and4_intro