(* Advanced constructions with pr_pat ***************************************)
(*** at_dec *)
-lemma pr_pat_dec (f) (i1) (i2): 𝐓❨f❩ → Decidable (@❨i1,f❩ ≘ i2).
+lemma pr_pat_dec (f) (i1) (i2): 𝐓❨f❩ → Decidable (@⧣❨i1,f❩ ≘ i2).
#f #i1 #i2 #Hf lapply (Hf i1) -Hf *
#j2 #Hf elim (eq_pnat_dec i2 j2)
[ #H destruct /2 width=1 by or_introl/
qed-.
(*** is_at_dec *)
-lemma is_pr_pat_dec (f) (i2): 𝐓❨f❩ → Decidable (∃i1. @❨i1,f❩ ≘ i2).
+lemma is_pr_pat_dec (f) (i2): 𝐓❨f❩ → Decidable (∃i1. @⧣❨i1,f❩ ≘ i2).
#f #i2 #Hf
-lapply (dec_plt (λi1.@❨i1,f❩ ≘ i2) … (↑i2)) [| * ]
+lapply (dec_plt (λi1.@⧣❨i1,f❩ ≘ i2) … (↑i2)) [| * ]
[ /2 width=1 by pr_pat_dec/
| * /3 width=2 by ex_intro, or_introl/
| #H @or_intror * #i1 #Hi12
(*** at_ext *)
corec theorem pr_eq_ext_pat (f1) (f2): 𝐓❨f1❩ → 𝐓❨f2❩ →
- (∀i,i1,i2. @❨i,f1❩ ≘ i1 → @❨i,f2❩ ≘ i2 → i1 = i2) →
+ (∀i,i1,i2. @⧣❨i,f1❩ ≘ i1 → @⧣❨i,f2❩ ≘ i2 → i1 = i2) →
f1 ≐ f2.
cases (pr_map_split_tl f1) #H1
cases (pr_map_split_tl f2) #H2