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=0b3ba39b001f5f7e1787537fb1cafa0c0ad1c200;hpb=00fca351072c2dba11b71c14b1169d303fd6836f;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 0b3ba39b0..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
@@ -39,19 +39,26 @@ lemma lift_term_after (f1) (f2) (t):
 ]
 qed.
 
-lemma lift_term_id_sn (t):
-      t ⊆ ↑[𝐢]t.
-#t #p #Hp
->(lift_path_id p)
-/2 width=1 by in_comp_lift_bi/
+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_id_dx (t):
-      ↑[𝐢]t ⊆ t.
-#t #p * #q #Hq #H destruct //
+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_id (t):
-      t ⇔ ↑[𝐢]t.
-/3 width=2 by lift_term_id_dx, lift_term_id_sn, conj/
-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.