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
index 1d3aeedf531dde6c74f190f1134522efaa2e3f33..5bb66e16ab112f1ab94db7db70cba521bc150131 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_constructors.ma
@@ -13,8 +13,9 @@
 (**************************************************************************)
 
 include "delayed_updating/syntax/prototerm.ma".
+include "delayed_updating/notation/functions/m_hook_1.ma".
 include "delayed_updating/notation/functions/hash_1.ma".
-include "delayed_updating/notation/functions/phi_2.ma".
+include "delayed_updating/notation/functions/tau_2.ma".
 include "delayed_updating/notation/functions/lamda_1.ma".
 include "delayed_updating/notation/functions/at_2.ma".
 
@@ -26,29 +27,50 @@ definition prototerm_node_0 (l): prototerm ≝
 definition prototerm_node_1 (l): prototerm → prototerm ≝
            λt,p. ∃∃q. q ϵ t & l◗q = p.
 
+definition prototerm_node_1_2 (l1) (l2): prototerm → prototerm ≝
+           λt,p. ∃∃q. q ϵ t & l1◗l2◗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
+  "mark (prototerm)"
+  'MHook t = (prototerm_node_1 label_m t).
+
 interpretation
   "outer variable reference by depth (prototerm)"
-  'Hash n = (prototerm_node_0 (label_node_d n)).
+  'Hash k = (prototerm_node_0 (label_d k)).
 
 interpretation
   "inner variable reference by depth (prototerm)"
-  'Phi n t = (prototerm_node_1 (label_node_d n) t).
+  'Tau k t = (prototerm_node_1_2 (label_d k) label_m t).
 
 interpretation
   "name-free functional abstraction (prototerm)"
-  'Lamda t = (prototerm_node_1 label_edge_L t).
+  'Lamda t = (prototerm_node_1 label_L t).
 
 interpretation
   "application (prototerm)"
-  'At u t = (prototerm_node_2 label_edge_S label_edge_A u t).
+  'At u t = (prototerm_node_2 label_S label_A u t).
+
+(* Basic constructions *******************************************************)
+
+lemma in_comp_iref (t) (q) (k):
+      q ϵ t → 𝗱k◗𝗺◗q ϵ 𝛕k.t.
+/2 width=3 by ex2_intro/ qed.
 
-(* Basic Inversions *********************************************************)
+(* Basic inversions *********************************************************)
 
+lemma in_comp_inv_iref (t) (p) (k):
+      p ϵ 𝛕k.t →
+      ∃∃q. 𝗱k◗𝗺◗q = p & q ϵ t.
+#t #p #k * #q #Hq #Hp
+/2 width=3 by ex2_intro/
+qed-.
+
+(* COMMENT
 lemma prototerm_in_root_inv_lcons_oref:
       ∀p,l,n. l◗p ϵ ▵#n →
       ∧∧ 𝗱n = l & 𝐞 = p.
@@ -59,18 +81,26 @@ elim (eq_inv_list_empty_append … e0) -e0 #H0 #_
 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
+      ∀t,p,l,n. l◗p ϵ ▵𝛕n.t →
+      ∧∧ 𝗱n = l & p ϵ ▵ɱ.t.
+#t #p #l #n * #q * #r #Hr
+<list_append_lcons_sn #H0 destruct -H0
+/4 width=4 by ex2_intro, ex_intro, conj/
+qed-.
+
+lemma prototerm_in_root_inv_lcons_mark:
+      ∀t,p,l. l◗p ϵ ▵ɱ.t →
+      ∧∧ 𝗺 = l & p ϵ ▵t.
+#t #p #l * #q * #r #Hr
+<list_append_lcons_sn #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
+#t #p #l * #q * #r #Hr
+<list_append_lcons_sn #H0 destruct
 /3 width=2 by ex_intro, conj/
 qed-.
 
@@ -78,7 +108,8 @@ 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
+#u #t #p #l * #q * * #r #Hr
+<list_append_lcons_sn #H0 destruct
 /4 width=2 by ex_intro, or_introl, or_intror, conj/
 qed-.
+*)