update in static_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / lifts.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma
index 54372cf8f4c0333fb8088c96a4b455309e71ec54..060f3b8057d843e509201ed69a526d62895c6f01 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma
@@ -56,6 +56,10 @@ definition deliftable2_bi: predicate (relation term) ≝
                            λR. ∀U1,U2. R U1 U2 → ∀f,T1. ⬆*[f] T1 ≘ U1 →
                            ∀T2. ⬆*[f] T2 ≘ U2 → R T1 T2.
 
+definition deliftable2_dx: predicate (relation term) ≝
+                           λR. ∀U1,U2. R U1 U2 → ∀f,T2. ⬆*[f] T2 ≘ U2 →
+                           ∃∃T1. ⬆*[f] T1 ≘ U1 & R T1 T2.
+
 (* Basic inversion lemmas ***************************************************)
 
 fact lifts_inv_sort1_aux: ∀f,X,Y. ⬆*[f] X ≘ Y → ∀s. X = ⋆s → Y = ⋆s.
@@ -329,6 +333,11 @@ qed-.
 
 (* Basic properties *********************************************************)
 
+lemma deliftable2_sn_dx (R): symmetric … R → deliftable2_sn R → deliftable2_dx R.
+#R #H2R #H1R #U1 #U2 #HU12 #f #T2 #HTU2
+elim (H1R … U1 … HTU2) -H1R /3 width=3 by ex2_intro/
+qed-.
+
 lemma lifts_eq_repl_back: ∀T1,T2. eq_repl_back … (λf. ⬆*[f] T1 ≘ T2).
 #T1 #T2 #f1 #H elim H -T1 -T2 -f1
 /4 width=5 by lifts_flat, lifts_bind, lifts_lref, at_eq_repl_back, eq_push/
@@ -356,6 +365,15 @@ elim (IHV1 f) -IHV1 #V2 #HV12
 ]
 qed-.
 
+lemma lifts_push_zero (f): ⬆*[⫯f]#O ≘ #0.
+/2 width=1 by lifts_lref/ qed.
+
+lemma lifts_push_lref (f) (i1) (i2): ⬆*[f]#i1 ≘ #i2 → ⬆*[⫯f]#(↑i1) ≘ #(↑i2).
+#f1 #i1 #i2 #H
+elim (lifts_inv_lref1 … H) -H #j #Hij #H destruct
+/3 width=7 by lifts_lref, at_push/
+qed.
+
 lemma lifts_lref_uni: ∀l,i. ⬆*[l] #i ≘ #(l+i).
 #l elim l -l /2 width=1 by lifts_lref/
 qed.