X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfeq.ma;h=684e57370908a1ac8abdd71a4b1b5b0c4d225043;hb=f7296f9cf2ee73465a374942c46b138f35c42ccb;hp=1b625752029bb6cdb6b5864a500d72c308e82ea2;hpb=775106f04b47236bf47e4321d745ec360ab4ebb4;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
index 1b6257520..684e57370 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
@@ -25,19 +25,44 @@ interpretation
    "syntactic equivalence on referred entries (local environment)"
    'LazyEqSn T L1 L2 = (lfeq T L1 L2).
 
+(* Note: "lfeq_transitive R" is equivalent to "lfxs_transitive ceq R R" *)
 (* Basic_2A1: uses: lleq_transitive *)
 definition lfeq_transitive: predicate (relation3 lenv term term) ≝
            λR. ∀L2,T1,T2. R L2 T1 T2 → ∀L1. L1 ≡[T1] L2 → R L1 T1 T2.
 
-(* Basic_properties *********************************************************)
+(* Basic inversion lemmas ***************************************************)
 
-lemma lfxs_transitive_lfeq: ∀R. lfxs_transitive ceq R R → lfeq_transitive R.
-/2 width=5 by/ qed.
+lemma lfeq_inv_bind: ∀p,I,L1,L2,V,T. L1 ≡[ⓑ{p,I}V.T] L2 →
+                     ∧∧ L1 ≡[V] L2 & L1.ⓑ{I}V ≡[T] L2.ⓑ{I}V.
+/2 width=2 by lfxs_inv_bind/ qed-.
 
-(* Basic inversion lemmas ***************************************************)
+lemma lfeq_inv_flat: ∀I,L1,L2,V,T. L1 ≡[ⓕ{I}V.T] L2 →
+                     ∧∧ L1 ≡[V] L2 & L1 ≡[T] L2.
+/2 width=2 by lfxs_inv_flat/ qed-.
+
+(* Advanced inversion lemmas ************************************************)
 
-lemma lfeq_transitive_inv_lfxs: ∀R. lfeq_transitive R → lfxs_transitive ceq R R.
-/2 width=3 by/ qed-.
+lemma lfeq_inv_zero_pair_sn: ∀I,L2,K1,V. K1.ⓑ{I}V ≡[#0] L2 →
+                             ∃∃K2. K1 ≡[V] K2 & L2 = K2.ⓑ{I}V.
+#I #L2 #K1 #V #H
+elim (lfxs_inv_zero_pair_sn … H) -H #K2 #X #HK12 #HX #H destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma lfeq_inv_zero_pair_dx: ∀I,L1,K2,V. L1 ≡[#0] K2.ⓑ{I}V →
+                             ∃∃K1. K1 ≡[V] K2 & L1 = K1.ⓑ{I}V.
+#I #L1 #K2 #V #H
+elim (lfxs_inv_zero_pair_dx … H) -H #K1 #X #HK12 #HX #H destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma lfeq_inv_lref_bind_sn: ∀I1,K1,L2,i. K1.ⓘ{I1} ≡[#⫯i] L2 →
+                             ∃∃I2,K2. K1 ≡[#i] K2 & L2 = K2.ⓘ{I2}.
+/2 width=2 by lfxs_inv_lref_bind_sn/ qed-.
+
+lemma lfeq_inv_lref_bind_dx: ∀I2,K2,L1,i. L1 ≡[#⫯i] K2.ⓘ{I2} →
+                             ∃∃I1,K1. K1 ≡[#i] K2 & L1 = K1.ⓘ{I1}.
+/2 width=2 by lfxs_inv_lref_bind_dx/ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
@@ -49,6 +74,32 @@ lemma lfeq_fwd_lfxs: ∀R. c_reflexive … R →
 /4 width=7 by lexs_co, cext2_co, ex2_intro/
 qed-.
 
+(* Basic_properties *********************************************************)
+
+lemma frees_lfeq_conf: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f →
+                       ∀L2. L1 ≡[T] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
+#f #L1 #T #H elim H -f -L1 -T
+[ /2 width=3 by frees_sort/
+| #f #i #Hf #L2 #H2
+  >(lfxs_inv_atom_sn … H2) -L2
+  /2 width=1 by frees_atom/
+| #f #I #L1 #V1 #_ #IH #Y #H2
+  elim (lfeq_inv_zero_pair_sn … H2) -H2 #L2 #HL12 #H destruct
+  /3 width=1 by frees_pair/
+| #f #I #L1 #Hf #Y #H2
+  elim (lfxs_inv_zero_unit_sn … H2) -H2 #g #L2 #_ #_ #H destruct
+  /2 width=1 by frees_unit/
+| #f #I #L1 #i #_ #IH #Y #H2
+  elim (lfeq_inv_lref_bind_sn … H2) -H2 #J #L2 #HL12 #H destruct
+  /3 width=1 by frees_lref/
+| /2 width=1 by frees_gref/
+| #f1V #f1T #f1 #p #I #L1 #V1 #T1 #_ #_ #Hf1 #IHV #IHT #L2 #H2
+  elim (lfeq_inv_bind … H2) -H2 /3 width=5 by frees_bind/
+| #f1V #f1T #f1 #I #L1 #V1 #T1 #_ #_ #Hf1 #IHV #IHT #L2 #H2
+  elim (lfeq_inv_flat … H2) -H2 /3 width=5 by frees_flat/
+]
+qed-.
+
 (* Basic_2A1: removed theorems 10:
               lleq_ind lleq_fwd_lref
               lleq_fwd_drop_sn lleq_fwd_drop_dx