partial update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / lift.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
index fa63286846e697621e2ac313b739825204abc2a5..0c083d99873a7776be55f8858951633022bdf0ed 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/relocation/tr_compose.ma".
-include "ground/relocation/tr_uni.ma".
+include "ground/relocation/tr_compose_pap.ma".
+include "ground/relocation/tr_uni_pap.ma".
 include "delayed_updating/syntax/path.ma".
 include "delayed_updating/notation/functions/uparrow_4.ma".
 include "delayed_updating/notation/functions/uparrow_2.ma".
@@ -109,6 +109,10 @@ lemma lift_path_m_sn (f) (p):
 
 (* Basic constructions with proj_rmap ***************************************)
 
+lemma lift_rmap_empty (f):
+      f = ↑[𝐞]f.
+// qed.
+
 lemma lift_rmap_d_sn (f) (p) (n):
       ↑[p](f∘𝐮❨ninj n❩) = ↑[𝗱n◗p]f.
 #f * // qed.
@@ -140,6 +144,34 @@ lemma lift_rmap_append (p2) (p1) (f):
 ]
 qed.
 
+(* Advanced constructions with proj_rmap and path_rcons *********************)
+
+lemma lift_rmap_d_dx (f) (p) (n):
+      (↑[p]f)∘𝐮❨ninj n❩ = ↑[p◖𝗱n]f.
+// qed.
+
+lemma lift_rmap_m_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗺]f.
+// qed.
+
+lemma lift_rmap_L_dx (f) (p):
+      (⫯↑[p]f) = ↑[p◖𝗟]f.
+// qed.
+
+lemma lift_rmap_A_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗔]f.
+// qed.
+
+lemma lift_rmap_S_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗦]f.
+// qed.
+
+lemma lift_rmap_pap_d_dx (f) (p) (n) (m):
+      ↑[p]f@❨m+n❩ = ↑[p◖𝗱n]f@❨m❩.
+#f #p #n #m
+<lift_rmap_d_dx <tr_compose_pap <tr_uni_pap //
+qed.
+
 (* Advanced eliminations with path ******************************************)
 
 lemma path_ind_lift (Q:predicate …):