(* COMMENT
axiom pippo (b) (q) (n):
- ↑❘q❘ = (↑[q]𝐢)@❨n❩ →
- ↑❘q❘+❘b❘= (↑[b●𝗟◗q]𝐢)@❨n+❘b❘❩.
+ ↑❘q❘ = (↑[q]𝐢)@⧣❨n❩ →
+ ↑❘q❘+❘b❘= (↑[b●𝗟◗q]𝐢)@⧣❨n+❘b❘❩.
lemma unwind_rmap_tls_eq_id (p) (n):
- ❘p❘ = ↑[p]𝐢@❨n❩ →
+ ❘p❘ = ↑[p]𝐢@⧣❨n❩ →
(𝐢) ≗ ⇂*[n]↑[p]𝐢.
#p @(list_ind_rcons … p) -p
[ #n <depth_empty #H destruct
]
-(* (↑❘q❘+❘b❘=↑[b●𝗟◗q]𝐢@❨n+❘b❘❩ *)
-(* [↑[p]𝐢@❨n❩]⫯*[❘p❘]f∘⇂*[n]↑[p]𝐢) *)
+(* (↑❘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❩ →
+ ❘p❘ = ↑[p]𝐢@⧣❨n❩ →
f ≗ ⇂*[n]↑[p]f.
#f #p #n #Hp
@(stream_eq_canc_dx … (stream_tls_eq_repl …))
]
(*
-Hn : ↑❘q❘ = ↑[p●𝗔◗b●𝗟◗q]𝐢@❨n❩
+Hn : ↑❘q❘ = ↑[p●𝗔◗b●𝗟◗q]𝐢@⧣❨n❩
---------------------------
-↑[𝐮❨↑❘q❘+❘b❘❩] ↑[↑[p]𝐢] t ⇔ ↑[𝐮❨↑[p●𝗔◗b●𝗟◗q]𝐢@❨n+❘b❘❩❩] t
+↑[𝐮❨↑❘q❘+❘b❘❩] ↑[↑[p]𝐢] t ⇔ ↑[𝐮❨↑[p●𝗔◗b●𝗟◗q]𝐢@⧣❨n+❘b❘❩❩] t
*)
(*
(↑[𝐮❨↑❘q❘❩]▼[⇂*[↑❘q❘]▼[p●𝗟◗q]𝐢](t1⋔(p◖𝗦))⇔▼[𝐮❨↑❘q❘❩∘▼[p●𝗔◗b●𝗟◗q]𝐢](t1⋔(p◖𝗦))