X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Frelocation%2Frtmap_isid.ma;h=65e111bbf9d3e209bbb6516965ff215c934dd339;hb=24ba1bb3f67505d3e384747ff90d26d3996bd3f5;hp=5ad6aa83c32edb6c8c37599dad3974473f5e4f8c;hpb=ad3d1cac216cf3882e4adf691b27c00838c6b9b1;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isid.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isid.ma
index 5ad6aa83c..65e111bbf 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isid.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isid.ma
@@ -43,7 +43,9 @@ lemma isid_inv_next: ∀g. 𝐈⦃g⦄ → ∀f. ⫯f = g → ⊥.
 #f #Hf * -g #g #H elim (discr_next_push … H)
 qed-.
 
-let corec isid_inv_eq_repl: ∀f1,f2. 𝐈⦃f1⦄ → 𝐈⦃f2⦄ → f1 ≗ f2 ≝ ?.
+(* Main inversion lemmas ****************************************************)
+
+corec theorem isid_inv_eq_repl: ∀f1,f2. 𝐈⦃f1⦄ → 𝐈⦃f2⦄ → f1 ≗ f2.
 #f1 #f2 #H1 #H2
 cases (isid_inv_gen … H1) -H1
 cases (isid_inv_gen … H2) -H2
@@ -52,7 +54,7 @@ qed-.
 
 (* Basic properties *********************************************************)
 
-let corec isid_eq_repl_back: eq_repl_back … isid ≝ ?.
+corec lemma isid_eq_repl_back: eq_repl_back … isid.
 #f1 #H cases (isid_inv_gen … H) -H
 #g1 #Hg1 #H1 #f2 #Hf cases (eq_inv_px … Hf … H1) -f1
 /3 width=3 by isid_push/
@@ -63,12 +65,39 @@ lemma isid_eq_repl_fwd: eq_repl_fwd … isid.
 
 (* Alternative definition ***************************************************)
 
-let corec eq_push_isid: ∀f. ↑f ≗ f → 𝐈⦃f⦄ ≝ ?.
+corec lemma eq_push_isid: ∀f. ↑f ≗ f → 𝐈⦃f⦄.
 #f #H cases (eq_inv_px … H) -H /4 width=3 by isid_push, eq_trans/
 qed.
 
-let corec eq_push_inv_isid: ∀f. 𝐈⦃f⦄ → ↑f ≗ f ≝ ?.
+corec lemma eq_push_inv_isid: ∀f. 𝐈⦃f⦄ → ↑f ≗ f.
 #f * -f
 #f #g #Hf #Hg @(eq_push … Hg) [2: @eq_push_inv_isid // | skip ]
 @eq_f //
 qed-.
+
+(* Properties with iterated push ********************************************)
+
+lemma isid_pushs: ∀n,f. 𝐈⦃f⦄ → 𝐈⦃↑*[n]f⦄.
+#n elim n -n /3 width=3 by isid_push/
+qed.
+
+(* Inversion lemmas with iterated push **************************************)
+
+lemma isid_inv_pushs: ∀n,g. 𝐈⦃↑*[n]g⦄ → 𝐈⦃g⦄.
+#n elim n -n /3 width=3 by isid_inv_push/
+qed.
+
+(* Properties with tail *****************************************************)
+
+lemma isid_tl: ∀f. 𝐈⦃f⦄ → 𝐈⦃⫱f⦄.
+#f cases (pn_split f) * #g * -f #H
+[ /2 width=3 by isid_inv_push/
+| elim (isid_inv_next … H) -H //
+]
+qed.
+
+(* Properties with iterated tail ********************************************)
+
+lemma isid_tls: ∀n,g. 𝐈⦃g⦄ → 𝐈⦃⫱*[n]g⦄.
+#n elim n -n /3 width=1 by isid_tl/
+qed.