update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind_k / unwind2_prototerm_constructors.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_prototerm_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_prototerm_constructors.ma
new file mode 100644 (file)
index 0000000..7a6d0ef
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_prototerm_constructors.ma
@@ -0,0 +1,62 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "delayed_updating/unwind_k/unwind2_prototerm_eq.ma".
+include "delayed_updating/unwind_k/unwind2_path_append.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+
+(* TAILED UNWIND FOR PROTOTERM **********************************************)
+
+(* Constructions with constructors for prototerm ****************************)
+
+lemma unwind2_term_oref_pap (f) (k):
+      (⧣(f＠⧣❨k❩)) ⇔ ▼[f]⧣k.
+#f #k @conj #p *
+[ /2 width=1 by in_comp_unwind2_path_term/
+| #q * #H0 destruct //
+]
+qed.
+
+lemma unwind2_term_iref (f) (t) (k:pnat):
+      ▼[f∘𝐮❨k❩]t ⇔ ▼[f](𝛕k.t).
+#f #t #k @conj
+#p * #q #Hq #H0 destruct
+[ @(ex2_intro … (𝗱k◗𝗺◗q))
+  /2 width=1 by in_comp_iref_hd/
+| elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
+  /2 width=1 by in_comp_unwind2_path_term/
+]
+qed.
+
+lemma unwind2_term_abst (f) (t):
+      (𝛌.▼[⫯f]t) ⇔ ▼[f]𝛌.t.
+#f #t @conj #p #Hp
+[ elim (in_comp_inv_abst … Hp) -Hp #q #H1 * #r #Hr #H2 destruct
+  /3 width=1 by in_comp_unwind2_path_term, in_comp_abst_hd/
+| elim Hp -Hp #q #Hq #H0 destruct
+  elim (in_comp_inv_abst … Hq) -Hq #r #H0 #Hr destruct
+  /3 width=1 by in_comp_unwind2_path_term, in_comp_abst_hd/
+]
+qed.
+
+lemma unwind2_term_appl (f) (v) (t):
+      ＠▼[f]v.▼[f]t ⇔ ▼[f]＠v.t.
+#f #v #t @conj #p #Hp
+[ elim (in_comp_inv_appl … Hp) -Hp * #q #H1 * #r #Hr #H2 destruct
+  /3 width=1 by in_comp_unwind2_path_term, in_comp_appl_sd, in_comp_appl_hd/
+| elim Hp -Hp #q #Hq #H0 destruct
+  elim (in_comp_inv_appl … Hq) -Hq * #r #H0 #Hr destruct
+  /3 width=1 by in_comp_unwind2_path_term, in_comp_appl_sd, in_comp_appl_hd/
+]
+qed.