X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfxs_lfxs.ma;h=89b84566be4e1e6aadced8a7c63dd302c36dbf69;hb=5c186c72f508da0849058afeecc6877cd9ed6303;hp=115d509ba0522885ac52985508b1c8249b84957d;hpb=47a745462a714af9d65cea7b61af56524bd98fa1;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
index 115d509ba..89b84566b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfxs_lfxs.ma
@@ -21,7 +21,7 @@ include "basic_2/static/lfxs.ma".
 (* Advanced inversion lemmas ************************************************)
 
 lemma lfxs_inv_frees: ∀R,L1,L2,T. L1 ⪤*[R, T] L2 →
-                      ∀f. L1 ⊢ 𝐅*⦃T⦄ ≡ f → L1 ⪤*[cext2 R, cfull, f] L2.
+                      ∀f. L1 ⊢ 𝐅*⦃T⦄ ≘ f → L1 ⪤*[cext2 R, cfull, f] L2.
 #R #L1 #L2 #T * /3 width=6 by frees_mono, lexs_eq_repl_back/
 qed-.
 
@@ -63,59 +63,6 @@ lapply (lexs_fwd_bind … Hf2) -Hf2 #Hf2 elim (sor_isfin_ex f1 (⫱f2))
 /3 width=7 by frees_fwd_isfin, frees_bind_void, lexs_join, isfin_tl, ex2_intro/
 qed.
 
-theorem lfxs_trans_gen: ∀R1,R2,R3. 
-                        c_reflexive … R1 → c_reflexive … R2 →
-                        lfxs_confluent R1 R2 → lfxs_transitive R1 R2 R3 →
-                        ∀L1,T,L. L1 ⪤*[R1, T] L →
-                        ∀L2. L ⪤*[R2, T] L2 → L1 ⪤*[R3, T] L2.
-#R1 #R2 #R3 #H1R #H2R #H3R #H4R #L1 #T @(fqup_wf_ind_eq (Ⓣ) … (⋆) L1 T) -L1 -T
-#G0 #L0 #T0 #IH #G #L1 * *
-[ #s #HG #HL #HT #L #H1 #L2 #H2 destruct
-  elim (lfxs_inv_sort … H1) -H1 *
-  [ #H1 #H0 destruct
-    >(lfxs_inv_atom_sn … H2) -L2 //
-  | #I1 #I #K1 #K #HK1 #H1 #H0 destruct
-    elim (lfxs_inv_sort_bind_sn … H2) -H2 #I2 #K2 #HK2 #H destruct
-    /4 width=3 by lfxs_sort, fqu_fqup/
-  ]
-| * [ | #i ] #HG #HL #HT #L #H1 #L2 #H2 destruct
-  [ elim (lfxs_inv_zero … H1) -H1 *
-    [ #H1 #H0 destruct
-      >(lfxs_inv_atom_sn … H2) -L2 //
-    | #I #K1 #K #V1 #V #HK1 #H1 #H0 #H destruct
-      elim (lfxs_inv_zero_pair_sn … H2) -H2 #K2 #V2 #HK2 #HV2 #H destruct
-      /4 width=7 by lfxs_pair, fqu_fqup, fqu_lref_O/
-    | #f1 #I #K1 #K #Hf1 #HK1 #H1 #H0 destruct
-      elim (lfxs_inv_zero_unit_sn … H2) -H2 #f2 #K2 #Hf2 #HK2 #H destruct
-      /5 width=8 by lfxs_unit, lexs_trans_id_cfull, lexs_eq_repl_back, isid_inv_eq_repl/
-    ]
-  | elim (lfxs_inv_lref … H1) -H1 *
-    [ #H1 #H0 destruct
-      >(lfxs_inv_atom_sn … H2) -L2 //
-    | #I1 #I #K1 #K #HK1 #H1 #H0 destruct
-      elim (lfxs_inv_lref_bind_sn … H2) -H2 #I2 #K2 #HK2 #H destruct
-     /4 width=3 by lfxs_lref, fqu_fqup/
-    ]
-  ]
-| #l #HG #HL #HT #L #H1 #L2 #H2 destruct
-  elim (lfxs_inv_gref … H1) -H1 *
-  [ #H1 #H0 destruct
-    >(lfxs_inv_atom_sn … H2) -L2 //
-  | #I1 #I #K1 #K #HK1 #H1 #H0 destruct
-    elim (lfxs_inv_gref_bind_sn … H2) -H2 #I2 #K2 #HK2 #H destruct
-    /4 width=3 by lfxs_gref, fqu_fqup/
-  ]
-| #p #I #V1 #T1 #HG #HL #HT #L #H1 #L2 #H2 destruct
-  elim (lfxs_inv_bind … V1 V1 … H1) -H1 // #H1V #H1T
-  elim (lfxs_inv_bind … V1 V1 … H2) -H2 // #H2V #H2T
-  /3 width=4 by lfxs_bind/
-| #I #V1 #T1 #HG #HL #HT #L #H1 #L2 #H2 destruct
-  elim (lfxs_inv_flat … H1) -H1 #H1V #H1T
-  elim (lfxs_inv_flat … H2) -H2 #H2V #H2T
-  /3 width=3 by lfxs_flat/
-]
-qed-.
-
 (* Negated inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: nllpx_sn_inv_bind nllpx_sn_inv_bind_O *)