update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
index 89ef40e91fdcc9362a7e7f6bb04ddf9926ea0d08..31f4bbc14b306af1e227e1acab1afe8c93242bc9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -17,26 +17,21 @@ include "delayed_updating/syntax/prototerm_constructors.ma".
 
 (* LIFT FOR PROTOTERM *******************************************************)
 
-lemma lift_iref_after_sn (f) (t:prototerm) (n:pnat):
-      ↑[f∘𝐮❨n❩]t ⊆ ↑[f](𝛗n.t).
-#f #t #n #p * #q #Hq #H0 destruct
-@(ex2_intro … (𝗱n◗𝗺◗q))
+lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
+      (𝛗f@❨n❩.↑[⇂*[n]f]t) ⊆ ↑[f](𝛗n.t).
+#f #t #n #p * #q * #r #Hr #H1 #H2 destruct
+@(ex2_intro … (𝗱n◗𝗺◗r))
 /2 width=1 by in_comp_iref/
 qed-.
 
-lemma lift_iref_after_dx (f) (t) (n:pnat):
-      ↑[f](𝛗n.t) ⊆ ↑[f∘𝐮❨n❩]t.
+lemma lift_iref_dx (f) (t) (n:pnat):
+      ↑[f](𝛗n.t) ⊆ 𝛗f@❨n❩.↑[⇂*[n]f]t.
 #f #t #n #p * #q #Hq #H0 destruct
-elim (in_comp_inv_iref … Hq) -Hq #p #Hp #Ht destruct
-/2 width=1 by in_comp_lift_bi/
+elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
+/3 width=1 by in_comp_iref, in_comp_lift_bi/
 qed-.
 
-lemma lift_iref_after (f) (t) (n:pnat):
-      ↑[f∘𝐮❨n❩]t ⇔ ↑[f](𝛗n.t).
-/3 width=1 by conj, lift_iref_after_sn, lift_iref_after_dx/
-qed.
-
 lemma lift_iref (f) (t) (n:pnat):
-      ↑[f]↑[𝐮❨n❩]t ⇔ ↑[f](𝛗n.t).
-/3 width=3 by lift_term_after, subset_eq_trans/
+      (𝛗f@❨n❩.↑[⇂*[n]f]t) ⇔ ↑[f](𝛗n.t).
+/3 width=1 by conj, lift_iref_sn, lift_iref_dx/
 qed.