(*** at_eq_repl_back *)
corec lemma pr_pat_eq_repl_back (i1) (i2):
- pr_eq_repl_back (λf. @❨i1,f❩ ≘ i2).
+ pr_eq_repl_back (λf. @⧣❨i1,f❩ ≘ i2).
#f1 * -f1 -i1 -i2
[ #f1 #g1 #j1 #j2 #H #H1 #H2 #f2 #H12
cases (pr_eq_inv_push_sn … H12 … H) -g1 /2 width=2 by pr_pat_refl/
(*** at_eq_repl_fwd *)
lemma pr_pat_eq_repl_fwd (i1) (i2):
- pr_eq_repl_fwd (λf. @❨i1,f❩ ≘ i2).
+ pr_eq_repl_fwd (λf. @⧣❨i1,f❩ ≘ i2).
#i1 #i2 @pr_eq_repl_sym /2 width=3 by pr_pat_eq_repl_back/
qed-.
-lemma pr_pat_eq (f): ⫯f ≐ f → ∀i. @❨i,f❩ ≘ i.
+lemma pr_pat_eq (f): ⫯f ≐ f → ∀i. @⧣❨i,f❩ ≘ i.
#f #Hf #i elim i -i
[ /3 width=3 by pr_pat_eq_repl_back, pr_pat_refl/
| /3 width=7 by pr_pat_eq_repl_back, pr_pat_push/
(* Inversions with pr_eq ****************************************************)
corec lemma pr_pat_inv_eq (f):
- (∀i. @❨i,f❩ ≘ i) → ⫯f ≐ f.
+ (∀i. @⧣❨i,f❩ ≘ i) → ⫯f ≐ f.
#Hf
lapply (Hf (𝟏)) #H
lapply (pr_pat_des_id … H) -H #H