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 31f4bbc14b306af1e227e1acab1afe8c93242bc9..772c837fb2866bfc1d3f3c7b9c80fefd2c7114cc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_constructors.ma
@@ -12,11 +12,17 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/substitution/lift_prototerm_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_id.ma".
+include "delayed_updating/substitution/lift_uni.ma".
 include "delayed_updating/syntax/prototerm_constructors.ma".
 
 (* LIFT FOR PROTOTERM *******************************************************)
 
+lemma lift_iref_bi (t1) (t2) (n):
+      t1 ⇔ t2 → 𝛗n.t1 ⇔ 𝛗n.t2.
+/2 width=1 by subset_equivalence_ext_f1_bi/
+qed.
+
 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
@@ -35,3 +41,11 @@ lemma lift_iref (f) (t) (n:pnat):
       (𝛗f@❨n❩.↑[⇂*[n]f]t) ⇔ ↑[f](𝛗n.t).
 /3 width=1 by conj, lift_iref_sn, lift_iref_dx/
 qed.
+
+lemma lift_iref_uni (t) (m) (n):
+      (𝛗(n+m).t) ⇔ ↑[𝐮❨m❩](𝛗n.t).
+#t #m #n
+@(subset_eq_trans … (lift_iref …))
+<tr_uni_pap >nsucc_pnpred <tr_tls_succ_uni
+/3 width=1 by lift_iref_bi, lift_term_id/
+qed.