X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsyntax%2Fpreterm.ma;h=6406d1dd7e50900f498b1832728315c5701e89e9;hb=41a54a797af98d2867d4bf979d424283fb44a1fc;hp=44d923d9bb742b2b8b49fc247031c9e8c40916d4;hpb=2e4a7c54ef77c10cb1cef4b59518c473245ea935;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/preterm.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/preterm.ma
index 44d923d9b..6406d1dd7 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/preterm.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/preterm.ma
@@ -12,25 +12,30 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/lib/subset.ma".
-include "delayed_updating/syntax/path.ma".
-include "delayed_updating/notation/functions/uptriangle_1.ma".
+include "delayed_updating/syntax/prototerm.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/notation/functions/class_t_0.ma".
 
 (* PRETERM ******************************************************************)
 
-(* Note: preterms are subsets of complete paths *)
-definition preterm: Type[0] ≝ 𝒫❨path❩.
-
-definition preterm_root: preterm → preterm ≝
-           λt,p. ∃q. p;;q ϵ t.
+(* Note: a preterm is a prototerm satislying the condition below *)
+(* Note: different root paths have different structure *)
+definition structure_injective: predicate prototerm ≝
+           λt. ∀p1,p2. p1 ϵ ▵t → p2 ϵ ▵t → ⊗p1 = ⊗p2 → p1 = p2
+.
 
 interpretation
-  "root (preterm)"
-  'UpTriangle t = (preterm_root t).
+  "preterm (prototerm)"
+  'ClassT = (structure_injective).
 
-(* Basic constructions ******************************************************)
+(* Basic inversions *********************************************************)
 
-lemma preterm_in_comp_root (p) (t):
-      p ϵ t → p ϵ ▵t.
-/2 width=2 by ex_intro/
-qed.
+lemma preterm_in_root_append_inv_structure_empty_dx (t) (p) (q):
+      p●q ϵ ▵t → t ϵ 𝐓 → 𝐞 = ⊗q → 𝐞 = q.
+#t #p #q #Hpq #Ht #Hq
+lapply (Ht p ?? Hpq ?)
+[ <structure_append //
+| /2 width=2 by prototerm_in_root_append_des_sn/
+| /2 width=3 by eq_inv_list_append_dx_dx_refl/
+]
+qed-.