- intermediate commit to allow debugging of auto tactic in xprs.ma

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / unfold / delift.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift.ma
index bb5b3ac4e8b4f8f73fd1c1d0e04c8fd13e87c212..3c9ecc3ca46a0125cded56d4f2666e8ac0ed06f6 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/delift.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/delift.ma
@@ -25,59 +25,59 @@ interpretation "inverse basic relocation (term)"
 (* Basic properties *********************************************************)
 
 lemma lift_delift: ∀T1,T2,d,e. ⇧[d, e] T1 ≡ T2 →
-                   ∀L. L ⊢ T2 ▼*[d, e] ≡ T1.
+                   ∀L. L ⊢ ▼*[d, e] T2 ≡ T1.
 /2 width=3/ qed.
 
-lemma delift_refl_O2: ∀L,T,d. L ⊢ T ▼*[d, 0] ≡ T.
+lemma delift_refl_O2: ∀L,T,d. L ⊢ ▼*[d, 0] T ≡ T.
 /2 width=3/ qed.
 
-lemma delift_lsubs_trans: ∀L1,T1,T2,d,e. L1 ⊢ T1 ▼*[d, e] ≡ T2 →
-                          ∀L2. L2 ≼ [d, e] L1 → L2 ⊢ T1 ▼*[d, e] ≡ T2.
+lemma delift_lsubs_trans: ∀L1,T1,T2,d,e. L1 ⊢ ▼*[d, e] T1 ≡ T2 →
+                          ∀L2. L2 ≼ [d, e] L1 → L2 ⊢ ▼*[d, e] T1 ≡ T2.
 #L1 #T1 #T2 #d #e * /3 width=3/
 qed.
 
-lemma delift_sort: â\88\80L,d,e,k. L â\8a¢ â\8b\86k â\96¼*[d, e] ≡ ⋆k.
+lemma delift_sort: â\88\80L,d,e,k. L â\8a¢ â\96¼*[d, e] â\8b\86k ≡ ⋆k.
 /2 width=3/ qed.
 
-lemma delift_lref_lt: ∀L,d,e,i. i < d → L ⊢ #i ▼*[d, e] ≡ #i.
+lemma delift_lref_lt: ∀L,d,e,i. i < d → L ⊢ ▼*[d, e] #i ≡ #i.
 /3 width=3/ qed.
 
-lemma delift_lref_ge: ∀L,d,e,i. d + e ≤ i → L ⊢ #i ▼*[d, e] ≡ #(i - e).
+lemma delift_lref_ge: ∀L,d,e,i. d + e ≤ i → L ⊢ ▼*[d, e] #i ≡ #(i - e).
 /3 width=3/ qed.
 
-lemma delift_gref: ∀L,d,e,p. L ⊢ §p ▼*[d, e] ≡ §p.
+lemma delift_gref: ∀L,d,e,p. L ⊢ ▼*[d, e] §p ≡ §p.
 /2 width=3/ qed.
 
 lemma delift_bind: ∀I,L,V1,V2,T1,T2,d,e.
-                   L ⊢ V1 ▼*[d, e] ≡ V2 → L. ⓑ{I} V2 ⊢ T1 ▼*[d+1, e] ≡ T2 →
-                   L â\8a¢ â\93\91{I} V1. T1 â\96¼*[d, e] ≡ ⓑ{I} V2. T2.
+                   L ⊢ ▼*[d, e] V1 ≡ V2 → L. ⓑ{I} V2 ⊢ ▼*[d+1, e] T1 ≡ T2 →
+                   L â\8a¢ â\96¼*[d, e] â\93\91{I} V1. T1 ≡ ⓑ{I} V2. T2.
 #I #L #V1 #V2 #T1 #T2 #d #e * #V #HV1 #HV2 * #T #HT1 #HT2
 lapply (tpss_lsubs_trans … HT1 (L. ⓑ{I} V) ?) -HT1 /2 width=1/ /3 width=5/
 qed.
 
 lemma delift_flat: ∀I,L,V1,V2,T1,T2,d,e.
-                   L ⊢ V1 ▼*[d, e] ≡ V2 → L ⊢ T1 ▼*[d, e] ≡ T2 →
-                   L â\8a¢ â\93\95{I} V1. T1 â\96¼*[d, e] ≡ ⓕ{I} V2. T2.
+                   L ⊢ ▼*[d, e] V1 ≡ V2 → L ⊢ ▼*[d, e] T1 ≡ T2 →
+                   L â\8a¢ â\96¼*[d, e] â\93\95{I} V1. T1 ≡ ⓕ{I} V2. T2.
 #I #L #V1 #V2 #T1 #T2 #d #e * #V #HV1 #HV2 * /3 width=5/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma delift_inv_sort1: â\88\80L,U2,d,e,k. L â\8a¢ â\8b\86k â\96¼*[d, e] ≡ U2 → U2 = ⋆k.
+lemma delift_inv_sort1: â\88\80L,U2,d,e,k. L â\8a¢ â\96¼*[d, e] â\8b\86k ≡ U2 → U2 = ⋆k.
 #L #U2 #d #e #k * #U #HU
 >(tpss_inv_sort1 … HU) -HU #HU2
 >(lift_inv_sort2 … HU2) -HU2 //
 qed-.
 
-lemma delift_inv_gref1: ∀L,U2,d,e,p. L ⊢ §p ▼*[d, e] ≡ U2 → U2 = §p.
+lemma delift_inv_gref1: ∀L,U2,d,e,p. L ⊢ ▼*[d, e] §p ≡ U2 → U2 = §p.
 #L #U #d #e #p * #U #HU
 >(tpss_inv_gref1 … HU) -HU #HU2
 >(lift_inv_gref2 … HU2) -HU2 //
 qed-.
 
-lemma delift_inv_bind1: â\88\80I,L,V1,T1,U2,d,e. L â\8a¢ â\93\91{I} V1. T1 â\96¼*[d, e] ≡ U2 →
-                        ∃∃V2,T2. L ⊢ V1 ▼*[d, e] ≡ V2 &
-                                 L. ⓑ{I} V2 ⊢ T1 ▼*[d+1, e] ≡ T2 &
+lemma delift_inv_bind1: â\88\80I,L,V1,T1,U2,d,e. L â\8a¢ â\96¼*[d, e] â\93\91{I} V1. T1 ≡ U2 →
+                        ∃∃V2,T2. L ⊢ ▼*[d, e] V1 ≡ V2 &
+                                 L. ⓑ{I} V2 ⊢ ▼*[d+1, e] T1 ≡ T2 &
                                  U2 = ⓑ{I} V2. T2.
 #I #L #V1 #T1 #U2 #d #e * #U #HU #HU2
 elim (tpss_inv_bind1 … HU) -HU #V #T #HV1 #HT1 #X destruct
@@ -85,16 +85,16 @@ elim (lift_inv_bind2 … HU2) -HU2 #V2 #T2 #HV2 #HT2
 lapply (tpss_lsubs_trans … HT1 (L. ⓑ{I} V2) ?) -HT1 /2 width=1/ /3 width=5/
 qed-.
 
-lemma delift_inv_flat1: â\88\80I,L,V1,T1,U2,d,e. L â\8a¢ â\93\95{I} V1. T1 â\96¼*[d, e] ≡ U2 →
-                        ∃∃V2,T2. L ⊢ V1 ▼*[d, e] ≡ V2 &
-                                 L ⊢ T1 ▼*[d, e] ≡ T2 &
+lemma delift_inv_flat1: â\88\80I,L,V1,T1,U2,d,e. L â\8a¢ â\96¼*[d, e] â\93\95{I} V1. T1 ≡ U2 →
+                        ∃∃V2,T2. L ⊢ ▼*[d, e] V1 ≡ V2 &
+                                 L ⊢ ▼*[d, e] T1 ≡ T2 &
                                  U2 = ⓕ{I} V2. T2.
 #I #L #V1 #T1 #U2 #d #e * #U #HU #HU2
 elim (tpss_inv_flat1 … HU) -HU #V #T #HV1 #HT1 #X destruct
 elim (lift_inv_flat2 … HU2) -HU2 /3 width=5/
 qed-.
 
-lemma delift_inv_refl_O2: ∀L,T1,T2,d. L ⊢ T1 ▼*[d, 0] ≡ T2 → T1 = T2.
+lemma delift_inv_refl_O2: ∀L,T1,T2,d. L ⊢ ▼*[d, 0] T1 ≡ T2 → T1 = T2.
 #L #T1 #T2 #d * #T #HT1
 >(tpss_inv_refl_O2 … HT1) -HT1 #HT2
 >(lift_inv_refl_O2 … HT2) -HT2 //
@@ -102,7 +102,7 @@ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma delift_fwd_tw: ∀L,T1,T2,d,e. L ⊢ T1 ▼*[d, e] ≡ T2 → #[T1] ≤ #[T2].
+lemma delift_fwd_tw: ∀L,T1,T2,d,e. L ⊢ ▼*[d, e] T1 ≡ T2 → #[T1] ≤ #[T2].
 #L #T1 #T2 #d #e * #T #HT1 #HT2
 >(tw_lift … HT2) -T2 /2 width=4 by tpss_fwd_tw /
 qed-.