update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / rtmap_isfin.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma
index 45c8ea854656683341e2106b4668ae3e741bcf3b..3a9d2656c7fbfacb4a982107d22334fc88582d38 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma
@@ -18,50 +18,79 @@ include "ground_2/relocation/rtmap_fcla.ma".
 (* RELOCATION MAP ***********************************************************)
 
 definition isfin: predicate rtmap ≝
-                  λf. â\88\83n. ð\9d\90\82â¦\83fâ¦\84 â\89¡ n.
+                  λf. â\88\83n. ð\9d\90\82â\9dªfâ\9d« â\89\98 n.
 
 interpretation "test for finite colength (rtmap)"
    'IsFinite f = (isfin f).
 
+(* 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 #IH1 #IH2 #IH3 #f #H elim H -H
+#n #H elim H -f -n /3 width=2 by ex_intro/
+qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma isfin_inv_push: ∀g. 𝐅❪g❫ → ∀f. ⫯f = g → 𝐅❪f❫.
+#g * /3 width=4 by fcla_inv_px, ex_intro/
+qed-.
+
+lemma isfin_inv_next: ∀g. 𝐅❪g❫ → ∀f. ↑f = g → 𝐅❪f❫.
+#g * #n #H #f #H0 elim (fcla_inv_nx … H … H0) -g
+/2 width=2 by ex_intro/
+qed-.
+
 (* Basic properties *********************************************************)
 
-lemma isfin_isid: ∀f. 𝐈⦃f⦄ → 𝐅⦃f⦄.
+lemma isfin_eq_repl_back: eq_repl_back … isfin.
+#f1 * /3 width=4 by fcla_eq_repl_back, ex_intro/
+qed-.
+
+lemma isfin_eq_repl_fwd: eq_repl_fwd … isfin.
+/3 width=3 by isfin_eq_repl_back, eq_repl_sym/ 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\91fâ¦\84.
+lemma isfin_push: â\88\80f. ð\9d\90\85â\9dªfâ\9d« â\86\92 ð\9d\90\85â\9dªâ«¯fâ\9d«.
 #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⫯fâ¦\84.
+lemma isfin_next: â\88\80f. ð\9d\90\85â\9dªfâ\9d« â\86\92 ð\9d\90\85â\9dªâ\86\91fâ\9d«.
 #f * /3 width=2 by fcla_next, ex_intro/
 qed.
 
-lemma isfin_eq_repl_back: eq_repl_back … isfin.
-#f1 * /3 width=4 by fcla_eq_repl_back, ex_intro/
-qed-.
+(* Properties with iterated push ********************************************)
 
-lemma isfin_eq_repl_fwd: eq_repl_fwd … isfin.
-/3 width=3 by isfin_eq_repl_back, eq_repl_sym/ qed-.
+lemma isfin_pushs: ∀n,f. 𝐅❪f❫ → 𝐅❪⫯*[n]f❫.
+#n elim n -n /3 width=3 by isfin_push/
+qed.
 
-(* Basic eliminators ********************************************************)
+(* Inversion lemmas with iterated push **************************************)
 
-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 #IH1 #IH2 #IH3 #f #H elim H -H
-#n #H elim H -f -n /3 width=2 by ex_intro/
-qed-.
+lemma isfin_inv_pushs: ∀n,g. 𝐅❪⫯*[n]g❫ → 𝐅❪g❫.
+#n elim n -n /3 width=3 by isfin_inv_push/
+qed.
 
-(* Basic inversion lemmas ***************************************************)
+(* Properties with tail *****************************************************)
 
-lemma isfin_inv_next: ∀g. 𝐅⦃g⦄ → ∀f. ⫯f = g → 𝐅⦃f⦄.
-#g * #n #H #f #H0 elim (fcla_inv_nx … H … H0) -g
-/2 width=2 by ex_intro/
+lemma isfin_tl: ∀f. 𝐅❪f❫ → 𝐅❪⫱f❫.
+#f elim (pn_split f) * #g #H #Hf destruct
+/3 width=3 by isfin_inv_push, isfin_inv_next/
+qed.
+
+(* Inversion lemmas with tail ***********************************************)
+
+lemma isfin_inv_tl: ∀f. 𝐅❪⫱f❫ → 𝐅❪f❫.
+#f elim (pn_split f) * /2 width=1 by isfin_next, isfin_push/
 qed-.
 
-(* Basic forward lemmas *****************************************************)
+(* Inversion lemmas with iterated tail **************************************)
 
-lemma isfin_fwd_push: ∀g. 𝐅⦃g⦄ → ∀f. ↑f = g → 𝐅⦃f⦄.
-#g * /3 width=4 by fcla_inv_px, ex_intro/
+lemma isfin_inv_tls: ∀n,f. 𝐅❪⫱*[n]f❫ → 𝐅❪f❫.
+#n elim n -n /3 width=1 by isfin_inv_tl/
 qed-.