update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / syntax / prototerm_constructors.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
new file mode 100644 (file)
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/syntax/prototerm.ma".
+include "delayed_updating/notation/functions/hash_1.ma".
+include "delayed_updating/notation/functions/phi_2.ma".
+include "delayed_updating/notation/functions/lamda_1.ma".
+include "delayed_updating/notation/functions/at_2.ma".
+
+(* CONSTRUCTORS FOR PROTOTERM ***********************************************)
+
+definition prototerm_node_0 (l): prototerm ≝
+           λp. l◗𝐞 = p.
+
+definition prototerm_node_1 (l): prototerm → prototerm ≝
+           λt,p. ∃∃q. q ϵ t & l◗q = p.
+
+definition prototerm_node_2 (l1) (l2): prototerm → prototerm → prototerm ≝
+           λt1,t2,p.
+           ∨∨ ∃∃q. q ϵ t1 & l1◗q = p
+            | ∃∃q. q ϵ t2 & l2◗q = p.
+
+interpretation
+  "outer variable reference by depth (prototerm)"
+  'Hash n = (prototerm_node_0 (label_node_d n)).
+
+interpretation
+  "inner variable reference by depth (prototerm)"
+  'Phi n t = (prototerm_node_1 (label_node_d n) t).
+
+interpretation
+  "name-free functional abstraction (prototerm)"
+  'Lamda t = (prototerm_node_1 label_edge_L t).
+
+interpretation
+  "application (prototerm)"
+  'At u t = (prototerm_node_2 label_edge_S label_edge_A u t).
+
+(* Basic Inversions *********************************************************)
+
+lemma prototerm_in_root_inv_lcons_oref:
+      ∀p,l,n. l◗p ϵ ▵#n →
+      ∧∧ 𝗱n = l & 𝐞 = p.
+#p #l #n * #q
+<list_append_lcons_sn #H0 destruct -H0
+elim (eq_inv_list_empty_append … e0) -e0 #H0 #_
+/2 width=1 by conj/
+qed-.
+
+lemma prototerm_in_root_inv_lcons_iref:
+      ∀t,p,l,n. l◗p ϵ ▵𝛗n.t →
+      ∧∧ 𝗱n = l & p ϵ ▵t.
+#t #p #l #n * #q
+<list_append_lcons_sn * #r #Hr #H0 destruct
+/3 width=2 by ex_intro, conj/
+qed-.
+
+lemma prototerm_in_root_inv_lcons_abst:
+      ∀t,p,l. l◗p ϵ ▵𝛌.t →
+      ∧∧ 𝗟 = l & p ϵ ▵t.
+#t #p #l * #q
+<list_append_lcons_sn * #r #Hr #H0 destruct
+/3 width=2 by ex_intro, conj/
+qed-.
+
+lemma prototerm_in_root_inv_lcons_appl:
+      ∀u,t,p,l. l◗p ϵ ▵@u.t →
+      ∨∨ ∧∧ 𝗦 = l & p ϵ ▵u
+       | ∧∧ 𝗔 = l & p ϵ ▵t.
+#u #t #p #l * #q
+<list_append_lcons_sn * * #r #Hr #H0 destruct
+/4 width=2 by ex_intro, or_introl, or_intror, conj/
+qed-.