X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsubstitution%2Flift_prototerm_eq.ma;h=afe2ddd0178edbbbc210c906fec0238f3b94ef4c;hb=74223db3fc45caccb3cfac80971b29cb0613da28;hp=fc3fb3fcf254e39abd1b194cb285f9a545c780a7;hpb=dfcad1c1a698bac1b7fb6a5f59393b28f45182af;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
index fc3fb3fcf..afe2ddd01 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_prototerm_eq.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "ground/lib/subset_ext_equivalence.ma".
-include "delayed_updating/substitution/lift_after.ma".
+include "delayed_updating/substitution/lift_path_after.ma".
 include "delayed_updating/substitution/lift_prototerm.ma".
 
 (* LIFT FOR PROTOTERM *******************************************************)
@@ -38,3 +38,27 @@ lemma lift_term_after (f1) (f2) (t):
 | @subset_equivalence_ext_f1_exteq /2 width=5/
 ]
 qed.
+
+lemma lift_term_grafted_sn (f) (t) (p):
+      ↑[↑[p]f](t⋔p) ⊆ (↑[f]t)⋔(↑[f]p).
+#f #t #p #q * #r #Hr #H0 destruct
+@(ex2_intro … Hr) -Hr
+<lift_path_append_sn //
+qed-.
+
+lemma lift_term_grafted_dx (f) (t) (p):
+      (↑[f]t)⋔(↑[f]p) ⊆ ↑[↑[p]f](t⋔p).
+#f #t #p #q * #r #Hr #H0
+elim (lift_path_inv_append_sn … (sym_eq … H0)) -H0
+#p0 #q0 #Hp0 #Hq0 #H0 destruct
+lapply (lift_path_inj … Hp0) -Hp0 #Hp0 destruct
+/2 width=1 by in_comp_lift_path_term/
+qed-.
+
+lemma lift_term_grafted (f) (t) (p):
+      ↑[↑[p]f](t⋔p) ⇔ (↑[f]t)⋔(↑[f]p).
+/3 width=1 by lift_term_grafted_sn, lift_term_grafted_dx, conj/ qed.
+
+lemma lift_term_grafted_S (f) (t) (p):
+      ↑[↑[p]f](t⋔(p◖𝗦)) ⇔ (↑[f]t)⋔((↑[f]p)◖𝗦).
+// qed.