(* Basic eliminators ********************************************************)
lemma isfin_ind (R:predicate rtmap): (∀f. 𝐈⦃f⦄ → R f) →
- (∀f. 𝐅⦃f⦄ → R f → R (↑f)) →
(∀f. 𝐅⦃f⦄ → R f → R (⫯f)) →
+ (∀f. 𝐅⦃f⦄ → R f → R (↑f)) →
∀f. 𝐅⦃f⦄ → R f.
#R #IH1 #IH2 #IH3 #f #H elim H -H
#n #H elim H -f -n /3 width=2 by ex_intro/
(* Basic inversion lemmas ***************************************************)
-lemma isfin_inv_push: â\88\80g. ð\9d\90\85â¦\83gâ¦\84 â\86\92 â\88\80f. â\86\91f = g → 𝐅⦃f⦄.
+lemma isfin_inv_push: â\88\80g. ð\9d\90\85â¦\83gâ¦\84 â\86\92 â\88\80f. ⫯f = g → 𝐅⦃f⦄.
#g * /3 width=4 by fcla_inv_px, ex_intro/
qed-.
-lemma isfin_inv_next: â\88\80g. ð\9d\90\85â¦\83gâ¦\84 â\86\92 â\88\80f. ⫯f = g → 𝐅⦃f⦄.
+lemma isfin_inv_next: â\88\80g. ð\9d\90\85â¦\83gâ¦\84 â\86\92 â\88\80f. â\86\91f = g → 𝐅⦃f⦄.
#g * #n #H #f #H0 elim (fcla_inv_nx … H … H0) -g
/2 width=2 by ex_intro/
qed-.
lemma isfin_isid: ∀f. 𝐈⦃f⦄ → 𝐅⦃f⦄.
/3 width=2 by fcla_isid, ex_intro/ qed.
-lemma isfin_push: â\88\80f. ð\9d\90\85â¦\83fâ¦\84 â\86\92 ð\9d\90\85â¦\83â\86\91f⦄.
+lemma isfin_push: â\88\80f. ð\9d\90\85â¦\83fâ¦\84 â\86\92 ð\9d\90\85â¦\83⫯f⦄.
#f * /3 width=2 by fcla_push, ex_intro/
qed.
-lemma isfin_next: â\88\80f. ð\9d\90\85â¦\83fâ¦\84 â\86\92 ð\9d\90\85â¦\83⫯f⦄.
+lemma isfin_next: â\88\80f. ð\9d\90\85â¦\83fâ¦\84 â\86\92 ð\9d\90\85â¦\83â\86\91f⦄.
#f * /3 width=2 by fcla_next, ex_intro/
qed.
(* Properties with iterated push ********************************************)
-lemma isfin_pushs: â\88\80n,f. ð\9d\90\85â¦\83fâ¦\84 â\86\92 ð\9d\90\85â¦\83â\86\91*[n]f⦄.
+lemma isfin_pushs: â\88\80n,f. ð\9d\90\85â¦\83fâ¦\84 â\86\92 ð\9d\90\85â¦\83⫯*[n]f⦄.
#n elim n -n /3 width=3 by isfin_push/
qed.
(* Inversion lemmas with iterated push **************************************)
-lemma isfin_inv_pushs: â\88\80n,g. ð\9d\90\85â¦\83â\86\91*[n]g⦄ → 𝐅⦃g⦄.
+lemma isfin_inv_pushs: â\88\80n,g. ð\9d\90\85â¦\83⫯*[n]g⦄ → 𝐅⦃g⦄.
#n elim n -n /3 width=3 by isfin_inv_push/
qed.