(* Destructions with cpp ****************************************************)
-lemma nap_plus_unwind2_rmap_closed (o) (f) (q) (m) (n):
- q ϵ 𝐂❨o,n❩ →
- f@§❨m❩+♭q = ▶[f]q@§❨m+n❩.
-#o #f #q #m #n #Hq elim Hq -q -n //
+lemma nap_plus_unwind2_rmap_closed (o) (e) (f) (q) (m) (n):
+ q ϵ 𝐂❨o,n,e❩ →
+ f@§❨m+e❩+♭q = ▶[f]q@§❨m+n❩.
+#o #e #f #q #m #n #Hq elim Hq -q -n //
#q #n [ #k #_ ] #_ #IH
[ <depth_d_dx <unwind2_rmap_d_dx
<tr_compose_nap <tr_uni_nap //
qed-.
lemma nap_unwind2_rmap_closed (o) (f) (q) (n):
- q ϵ 𝐂❨o,n❩ →
+ q ϵ 𝐂❨o,n,𝟎❩ →
f@§❨𝟎❩+♭q = ▶[f]q@§❨n❩.
#o #f #q #n #Hn
/2 width=2 by nap_plus_unwind2_rmap_closed/
qed-.
lemma nap_plus_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (m) (n):
- q ϵ 𝐂❨o,n❩ →
+ q ϵ 𝐂❨o,n,𝟎❩ →
(⫯▶[f]p)@§❨m❩+♭q = ▶[f](p●𝗟◗q)@§❨m+n❩.
#o #f #p #q #m #n #Hn
/2 width=2 by nap_plus_unwind2_rmap_closed/
qed-.
lemma nap_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
- q ϵ 𝐂❨o,n❩ →
+ q ϵ 𝐂❨o,n,𝟎❩ →
♭q = ▶[f](p●𝗟◗q)@§❨n❩.
#o #f #p #q #n #Hn
>(nplus_zero_sn n)
qed-.
lemma tls_succ_plus_unwind2_rmap_push_closed (o) (f) (q) (n):
- q ϵ 𝐂❨o,n❩ →
+ q ϵ 𝐂❨o,n,𝟎❩ →
∀m. ⇂*[m]f ≗ ⇂*[↑(m+n)]▶[⫯f]q.
#o #f #q #n #Hn elim Hn -q -n //
#q #n #k #_ #_ #IH #m
qed-.
lemma tls_succ_unwind2_rmap_push_closed (o) (f) (q) (n):
- q ϵ 𝐂❨o,n❩ →
+ q ϵ 𝐂❨o,n,𝟎❩ →
f ≗ ⇂*[↑n]▶[⫯f]q.
#o #f #q #n #Hn
/2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/
qed-.
lemma tls_succ_plus_unwind2_rmap_append_closed_Lq_dx (o) (f) (p) (q) (n):
- q ϵ 𝐂❨o,n❩ →
+ q ϵ 𝐂❨o,n,𝟎❩ →
∀m. ⇂*[m]▶[f]p ≗ ⇂*[↑(m+n)]▶[f](p●𝗟◗q).
#o #f #p #q #n #Hn #m
/2 width=2 by tls_succ_plus_unwind2_rmap_push_closed/
qed-.
lemma tls_succ_unwind2_rmap_closed (f) (q) (n):
- q ϵ 𝐂❨Ⓕ,n❩ →
+ q ϵ 𝐂❨Ⓕ,n,𝟎❩ →
⇂f ≗ ⇂*[↑n]▶[f]q.
#f #q #n #Hn
@(stream_eq_canc_dx … (stream_tls_eq_repl …))