(*** coafter_tls *)
lemma pr_coafter_tls_bi_tls (n2) (n1):
- ∀f1,f2,f. @↑❨n1, f1❩ ≘ n2 →
+ ∀f1,f2,f. @§❨n1, f1❩ ≘ n2 →
f1 ~⊚ f2 ≘ f → ⫰*[n2]f1 ~⊚ ⫰*[n1]f2 ≘ ⫰*[n2]f.
#n2 @(nat_ind_succ … n2) -n2 [ #n1 | #n2 #IH * [| #n1 ] ] #f1 #f2 #f #Hf1 #Hf
[ elim (pr_nat_inv_zero_dx … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1 destruct //
(*** coafter_tls_O *)
lemma pr_coafter_tls_sn_tls:
- ∀n,f1,f2,f. @↑❨𝟎, f1❩ ≘ n →
+ ∀n,f1,f2,f. @§❨𝟎, f1❩ ≘ n →
f1 ~⊚ f2 ≘ f → ⫰*[n]f1 ~⊚ f2 ≘ ⫰*[n]f.
/2 width=1 by pr_coafter_tls_bi_tls/ qed.