(* Note: this requires ↑ on third n2 *)
(*** at_tls *)
-lemma pr_pat_tls (n2) (f): ⫯⫰*[â\86\91n2]f â\89¡ ⫰*[n2]f → ∃i1. @❨i1,f❩ ≘ ↑n2.
+lemma pr_pat_tls (n2) (f): ⫯⫰*[â\86\91n2]f â\89\90 ⫰*[n2]f → ∃i1. @❨i1,f❩ ≘ ↑n2.
#n2 @(nat_ind_succ … n2) -n2
[ /4 width=4 by pr_pat_eq_repl_back, pr_pat_refl, ex_intro/
| #n2 #IH #f <pr_tls_swap <pr_tls_swap in ⊢ (??%→?); #H
(* Note: this requires ↑ on first n2 *)
(*** at_inv_tls *)
lemma pr_pat_inv_succ_dx_tls (n2) (i1) (f):
- @â\9d¨i1,fâ\9d© â\89\98 â\86\91n2 â\86\92 ⫯⫰*[â\86\91n2]f â\89¡ ⫰*[n2]f.
+ @â\9d¨i1,fâ\9d© â\89\98 â\86\91n2 â\86\92 ⫯⫰*[â\86\91n2]f â\89\90 ⫰*[n2]f.
#n2 @(nat_ind_succ … n2) -n2
[ #i1 #f #Hf elim (pr_pat_inv_unit_dx … Hf) -Hf // #g #H1 #H destruct
/2 width=1 by pr_eq_refl/