X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsyntax%2Fpreterm.ma;h=aabb5adae086e3bf10d98b1fe4f87783c8c3bda1;hb=9605ffc88831066a901ea4eb8e419f277662f372;hp=1da2d0174a8ddc1f188b5dadbc9131620bfc4968;hpb=3c257bf84769adf162510ed86a89872e3003629a;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 1da2d0174..aabb5adae 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/preterm.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/preterm.ma
@@ -12,31 +12,33 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground/lib/subset.ma".
 include "delayed_updating/syntax/path.ma".
-include "delayed_updating/notation/relations/up_down_arrow_epsilon_2.ma".
-include "delayed_updating/notation/relations/up_arrow_epsilon_2.ma".
+include "delayed_updating/notation/functions/pitchfork_2.ma".
+include "delayed_updating/notation/functions/uptriangle_1.ma".
 
 (* PRETERM ******************************************************************)
 
-definition preterm: Type[0] ≝ predicate path.
+(* Note: preterms are subsets of complete paths *)
+definition preterm: Type[0] ≝ 𝒫❨path❩.
 
-definition preterm_in_comp: relation2 path preterm ≝
-           λp,t. t p.
+definition preterm_grafted: path → preterm → preterm ≝
+           λp,t,q. p;;q ϵ t.
 
 interpretation
-  "belongs to complete (preterm)"
-  'UpDownArrowEpsilon p t = (preterm_in_comp p t).
+  "grafted (preterm)"
+  'Pitchfork t p = (preterm_grafted p t).
 
-definition preterm_in_root: relation2 path preterm ≝
-           λp,t. ∃q. p;;q ϵ⬦ t.
+definition preterm_root: preterm → preterm ≝
+           λt,q. ∃r. q;;r ϵ t.
 
 interpretation
-  "belongs to root (preterm)"
-  'UpArrowEpsilon p t = (preterm_in_root p t).
+  "root (preterm)"
+  'UpTriangle t = (preterm_root t).
 
 (* Basic constructions ******************************************************)
 
 lemma preterm_in_comp_root (p) (t):
-      p ϵ⬦ t → p ϵ▵ t.
+      p ϵ t → p ϵ ▵t.
 /2 width=2 by ex_intro/
 qed.