lemma tls_plus_lift_rmap_closed (o) (f) (q) (n):
q Ļµ šāØo,nā© ā
- ām. ā*[m]f ā ā*[m+n]ā[q]f.
+ ām. ā*[m]f ā ā*[m+n]š ¢[f]q.
#o #f #q #n #Hq elim Hq -q -n //
#q #n #_ #IH #m
<nplus_succ_dx <stream_tls_swap //
lemma tls_lift_rmap_closed (o) (f) (q) (n):
q Ļµ šāØo,nā© ā
- f ā ā*[n]ā[q]f.
+ f ā ā*[n]š ¢[f]q.
#o #f #q #n #H0
/2 width=2 by tls_plus_lift_rmap_closed/
qed-.
lemma tls_succ_lift_rmap_append_L_closed_dx (o) (f) (p) (q) (n):
q Ļµ šāØo,nā© ā
- ā[p]f ā ā*[ān]ā[pāšāq]f.
+ š ¢[f]p ā ā*[ān]š ¢[f](pāšāq).
#o #f #p #q #n #Hq
/3 width=2 by tls_lift_rmap_closed, pcc_L_sn/
qed-.