- advances towards strong normalization

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lifts.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma
index be42c0ebfa4d1742cd0bf70f57d2062b9dffa9b5..31f416f12fcec83c6a36b10efd450b9cbf25580c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts.ma
@@ -15,7 +15,7 @@
 
 include "ground_2/relocation/nstream_after.ma".
 include "basic_2/notation/relations/rliftstar_3.ma".
-include "basic_2/grammar/term.ma".
+include "basic_2/syntax/term.ma".
 
 (* GENERIC RELOCATION FOR TERMS *********************************************)
 
@@ -41,6 +41,21 @@ interpretation "uniform relocation (term)"
 interpretation "generic relocation (term)"
    'RLiftStar f T1 T2 = (lifts f T1 T2).
 
+definition liftable2_sn: predicate (relation term) ≝
+                         λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⬆*[f] T1 ≡ U1 → 
+                         ∃∃U2. ⬆*[f] T2 ≡ U2 & R U1 U2.
+
+definition deliftable2_sn: predicate (relation term) ≝
+                           λR. ∀U1,U2. R U1 U2 → ∀f,T1. ⬆*[f] T1 ≡ U1 →
+                           ∃∃T2. ⬆*[f] T2 ≡ U2 & R T1 T2.
+
+definition liftable2_bi: predicate (relation term) ≝
+                         λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⬆*[f] T1 ≡ U1 → 
+                         ∀U2. ⬆*[f] T2 ≡ U2 → R U1 U2.
+
+definition deliftable2_bi: predicate (relation term) ≝
+                           λR. ∀U1,U2. R U1 U2 → ∀f,T1. ⬆*[f] T1 ≡ U1 →
+                           ∀T2. ⬆*[f] T2 ≡ U2 → R T1 T2.
 
 (* Basic inversion lemmas ***************************************************)
 
@@ -265,10 +280,28 @@ lemma lifts_inv_pair_xy_y: ∀I,T,V,f. ⬆*[f] ②{I}V.T ≡ T → ⊥.
 ]
 qed-.
 
+(* Inversion lemmas with uniform relocations ********************************)
+
 lemma lifts_inv_lref1_uni: ∀l,Y,i. ⬆*[l] #i ≡ Y → Y = #(l+i).
 #l #Y #i1 #H elim (lifts_inv_lref1 … H) -H /4 width=4 by at_mono, eq_f/
 qed-.
 
+lemma lifts_inv_lref2_uni: ∀l,X,i2. ⬆*[l] X ≡ #i2 →
+                           ∃∃i1. X = #i1 & i2 = l + i1.
+#l #X #i2 #H elim (lifts_inv_lref2 … H) -H
+/3 width=3 by at_inv_uni, ex2_intro/
+qed-.
+
+lemma lifts_inv_lref2_uni_ge: ∀l,X,i. ⬆*[l] X ≡ #(l + i) → X = #i.
+#l #X #i2 #H elim (lifts_inv_lref2_uni … H) -H
+#i1 #H1 #H2 destruct /4 width=2 by injective_plus_r, eq_f, sym_eq/
+qed-.
+
+lemma lifts_inv_lref2_uni_lt: ∀l,X,i. ⬆*[l] X ≡ #i → i < l → ⊥.
+#l #X #i2 #H elim (lifts_inv_lref2_uni … H) -H
+#i1 #_ #H1 #H2 destruct /2 width=4 by lt_le_false/
+qed-.
+
 (* Basic forward lemmas *****************************************************)
 
 (* Basic_2A1: includes: lift_inv_O2 *)