X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfdeq_lfdeq.ma;h=3dab077cfb29ced6ccb8be8ed37bb3df3bcdd9a9;hb=5c186c72f508da0849058afeecc6877cd9ed6303;hp=71b1c0d4f668c84bad3295e3ae5f6ae7d1afa745;hpb=b4b5f03ffca4f250a1dc02f277b70e4f33ac8a9b;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_lfdeq.ma
index 71b1c0d4f..3dab077cf 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq_lfdeq.ma
@@ -12,43 +12,89 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/syntax/ext2_ext2.ma".
 include "basic_2/syntax/tdeq_tdeq.ma".
-include "basic_2/static/lfxs_lfxs.ma".
-include "basic_2/static/lfdeq.ma".
+include "basic_2/static/lfdeq_length.ma".
 
 (* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
 
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: lleq_sym *)
+lemma lfdeq_sym: ∀h,o,T. symmetric … (lfdeq h o T).
+/3 width=3 by lfdeq_fsge_comp, lfxs_sym, tdeq_sym/ qed-.
+
+(* Basic_2A1: uses: lleq_dec *)
+lemma lfdeq_dec: ∀h,o,L1,L2. ∀T:term. Decidable (L1 ≛[h, o, T] L2).
+/3 width=1 by lfxs_dec, tdeq_dec/ qed-.
+
 (* Main properties **********************************************************)
 
+(* Basic_2A1: uses: lleq_bind lleq_bind_O *) 
 theorem lfdeq_bind: ∀h,o,p,I,L1,L2,V1,V2,T.
-                    L1 ≡[h, o, V1] L2 → L1.ⓑ{I}V1 ≡[h, o, T] L2.ⓑ{I}V2 →
-                    L1 ≡[h, o, ⓑ{p,I}V1.T] L2.
+                    L1 ≛[h, o, V1] L2 → L1.ⓑ{I}V1 ≛[h, o, T] L2.ⓑ{I}V2 →
+                    L1 ≛[h, o, ⓑ{p,I}V1.T] L2.
 /2 width=2 by lfxs_bind/ qed.
 
-theorem lfdeq_flat: ∀h,o,I,L1,L2,V,T. L1 ≡[h, o, V] L2 → L1 ≡[h, o, T] L2 →
-                    L1 ≡[h, o, ⓕ{I}V.T] L2.
+(* Basic_2A1: uses: lleq_flat *)
+theorem lfdeq_flat: ∀h,o,I,L1,L2,V,T. L1 ≛[h, o, V] L2 → L1 ≛[h, o, T] L2 →
+                    L1 ≛[h, o, ⓕ{I}V.T] L2.
 /2 width=1 by lfxs_flat/ qed.
 
+theorem lfdeq_bind_void: ∀h,o,p,I,L1,L2,V,T.
+                         L1 ≛[h, o, V] L2 → L1.ⓧ ≛[h, o, T] L2.ⓧ →
+                         L1 ≛[h, o, ⓑ{p,I}V.T] L2.
+/2 width=1 by lfxs_bind_void/ qed.
+
+(* Basic_2A1: uses: lleq_trans *)
 theorem lfdeq_trans: ∀h,o,T. Transitive … (lfdeq h o T).
 #h #o #T #L1 #L * #f1 #Hf1 #HL1 #L2 * #f2 #Hf2 #HL2
-lapply (frees_tdeq_conf_lexs … Hf1 T … HL1) // #H0
+lapply (frees_tdeq_conf_lfdeq … Hf1 T … HL1) // #H0
 lapply (frees_mono … Hf2 … H0) -Hf2 -H0
-/4 width=7 by lexs_trans, lexs_eq_repl_back, tdeq_trans, ex2_intro/
+/5 width=7 by lexs_trans, lexs_eq_repl_back, tdeq_trans, ext2_trans, ex2_intro/
 qed-.
 
+(* Basic_2A1: uses: lleq_canc_sn *)
 theorem lfdeq_canc_sn: ∀h,o,T. left_cancellable … (lfdeq h o T).
 /3 width=3 by lfdeq_trans, lfdeq_sym/ qed-.
 
+(* Basic_2A1: uses: lleq_canc_dx *)
 theorem lfdeq_canc_dx: ∀h,o,T. right_cancellable … (lfdeq h o T).
 /3 width=3 by lfdeq_trans, lfdeq_sym/ qed-.
 
-(* Advanced properies on negated lazy equivalence *****************************)
+theorem lfdeq_repl: ∀h,o,L1,L2. ∀T:term. L1 ≛[h, o, T] L2 →
+                    ∀K1. L1 ≛[h, o, T] K1 → ∀K2. L2 ≛[h, o, T] K2 → K1 ≛[h, o, T] K2.
+/3 width=3 by lfdeq_canc_sn, lfdeq_trans/ qed-.
+
+(* Negated properties *******************************************************)
 
-(* Note: auto works with /4 width=8/ so lfdeq_canc_sn is preferred ************) 
-lemma lfdeq_nlfdeq_trans: ∀h,o.∀T:term.∀L1,L. L1 ≡[h, o, T] L →
-                          ∀L2. (L ≡[h, o, T] L2 → ⊥) → (L1 ≡[h, o, T] L2 → ⊥).
+(* Note: auto works with /4 width=8/ so lfdeq_canc_sn is preferred **********) 
+(* Basic_2A1: uses: lleq_nlleq_trans *)
+lemma lfdeq_lfdneq_trans: ∀h,o.∀T:term.∀L1,L. L1 ≛[h, o, T] L →
+                          ∀L2. (L ≛[h, o, T] L2 → ⊥) → (L1 ≛[h, o, T] L2 → ⊥).
 /3 width=3 by lfdeq_canc_sn/ qed-.
 
-lemma nlfdeq_lfdeq_div: ∀h,o.∀T:term.∀L2,L. L2 ≡[h, o, T] L →
-                        ∀L1. (L1 ≡[h, o, T] L → ⊥) → (L1 ≡[h, o, T] L2 → ⊥).
+(* Basic_2A1: uses: nlleq_lleq_div *)
+lemma lfdneq_lfdeq_div: ∀h,o.∀T:term.∀L2,L. L2 ≛[h, o, T] L →
+                        ∀L1. (L1 ≛[h, o, T] L → ⊥) → (L1 ≛[h, o, T] L2 → ⊥).
 /3 width=3 by lfdeq_trans/ qed-.
+
+theorem lfdneq_lfdeq_canc_dx: ∀h,o,L1,L. ∀T:term. (L1 ≛[h, o, T] L → ⊥) →
+                              ∀L2. L2 ≛[h, o, T] L → L1 ≛[h, o, T] L2 → ⊥.
+/3 width=3 by lfdeq_trans/ qed-.
+
+(* Negated inversion lemmas *************************************************)
+
+(* Basic_2A1: uses: nlleq_inv_bind nlleq_inv_bind_O *)
+lemma lfdneq_inv_bind: ∀h,o,p,I,L1,L2,V,T. (L1 ≛[h, o, ⓑ{p,I}V.T] L2 → ⊥) →
+                       (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1.ⓑ{I}V ≛[h, o, T] L2.ⓑ{I}V → ⊥).
+/3 width=2 by lfnxs_inv_bind, tdeq_dec/ qed-.
+
+(* Basic_2A1: uses: nlleq_inv_flat *)
+lemma lfdneq_inv_flat: ∀h,o,I,L1,L2,V,T. (L1 ≛[h, o, ⓕ{I}V.T] L2 → ⊥) →
+                       (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1 ≛[h, o, T] L2 → ⊥).
+/3 width=2 by lfnxs_inv_flat, tdeq_dec/ qed-.
+
+lemma lfdneq_inv_bind_void: ∀h,o,p,I,L1,L2,V,T. (L1 ≛[h, o, ⓑ{p,I}V.T] L2 → ⊥) →
+                            (L1 ≛[h, o, V] L2 → ⊥) ∨ (L1.ⓧ ≛[h, o, T] L2.ⓧ → ⊥).
+/3 width=3 by lfnxs_inv_bind_void, tdeq_dec/ qed-.