- some refactoring and minor additions

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cpx_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
index dc5466d629f3e7a4965bc70e5ed6b2681f670266..f21e359595a9d65d35fba2d42ce88d7c56083965 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_lleq.ma
@@ -12,42 +12,44 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/ldrop_leq.ma".
-include "basic_2/relocation/lleq_lleq.ma".
-include "basic_2/reduction/cpx.ma".
+include "basic_2/multiple/lleq_ldrop.ma".
+include "basic_2/reduction/cpx_llpx_sn.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
 
 (* Properties on lazy equivalence for local environments ********************)
 
-lemma lleq_cpx_trans_leq: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
-                          ∀L1,d. L1 ⋕[d, T1] L2 → L1 ≃[d, ∞] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
-#h #g #G #L2 #T1 #T2 #H elim H -G -L2 -T1 -T2 /2 width=2 by cpx_sort/
-[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #d #H #HL12 elim (lleq_inv_lref_dx … H … HLK2) -H *
-  [ #K1 #HLK1 #HV1 #Hdi elim (ldrop_leq_conf_be … HL12 … HLK1) -HL12 /2 width=1 by yle_inj/
-    >yminus_Y_inj #J #Y #X #HK12 #H lapply (ldrop_mono … H … HLK2) -L2
-    #H destruct /3 width=7 by cpx_delta/
-  | #J #K1 #V #HLK1 #_ #HV1 #Hid elim (ldrop_leq_conf_lt … HL12 … HLK1) -HL12 /2 width=1 by ylt_inj/
-    #Y #HK12 #H lapply (ldrop_mono … H … HLK2) -L2
-    #H destruct /3 width=7 by cpx_delta/
+lemma lleq_cpx_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
+                      ∀L1. L1 ≡[T1, 0] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
+#h #g #G #L2 #T1 #T2 #H elim H -G -L2 -T1 -T2 /2 width=2 by cpx_st/
+[ #I #G #L2 #K2 #V1 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV12 #L1 #H elim (lleq_fwd_lref_dx … H … HLK2) -L2
+  [ #H elim (ylt_yle_false … H) //
+  | * /3 width=7 by cpx_delta/
   ]
-| #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #d #H elim (lleq_inv_bind … H) -H
-  /4 width=3 by cpx_bind, leq_succ/
-| #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #d #H elim (lleq_inv_flat … H) -H
-  /3 width=3 by cpx_flat/
-| #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #d #H elim (lleq_inv_bind … H) -H
-  /4 width=3 by cpx_zeta, leq_succ/
-| #G #L2 #W1 #T1 #T2 #_ #IHT12 #L1 #d #H elim (lleq_inv_flat … H) -H
-  /3 width=3 by cpx_tau/
-| #G #L2 #W1 #W2 #T1 #_ #IHW12 #L1 #d #H elim (lleq_inv_flat … H) -H
-  /3 width=3 by cpx_ti/
-| #a #G #L1 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #d #H elim (lleq_inv_flat … H) -H
-  #HV1 #H elim (lleq_inv_bind … H) -H /4 width=3 by cpx_beta, leq_succ/
-| #a #G #L1 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #d #H elim (lleq_inv_flat … H) -H
-  #HV1 #H elim (lleq_inv_bind … H) -H /4 width=3 by cpx_theta, leq_succ/
+| #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_bind_O … H) -H
+  /3 width=1 by cpx_bind/
+| #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
+  /3 width=1 by cpx_flat/
+| #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #H elim (lleq_inv_bind_O … H) -H
+  /3 width=3 by cpx_zeta/
+| #G #L2 #W1 #T1 #T2 #_ #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
+  /3 width=1 by cpx_eps/
+| #G #L2 #W1 #W2 #T1 #_ #IHW12 #L1 #H elim (lleq_inv_flat … H) -H
+  /3 width=1 by cpx_ct/
+| #a #G #L1 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
+  #HV1 #H elim (lleq_inv_bind_O … H) -H /3 width=1 by cpx_beta/
+| #a #G #L1 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #H elim (lleq_inv_flat … H) -H
+  #HV1 #H elim (lleq_inv_bind_O … H) -H /3 width=3 by cpx_theta/
 ]
 qed-.
 
-lemma lleq_cpx_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
-                      ∀L1. L1 ⋕[0, T1] L2 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
-/4 width=6 by lleq_cpx_trans_leq, lleq_fwd_length, leq_O_Y/ qed-. 
+lemma cpx_lleq_conf: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
+                     ∀L1. L2 ≡[T1, 0] L1 → ⦃G, L1⦄ ⊢ T1 ➡[h, g] T2.
+/3 width=3 by lleq_cpx_trans, lleq_sym/ qed-.
+
+lemma cpx_lleq_conf_sn: ∀h,g,G. s_r_confluent1 … (cpx h g G) (lleq 0).
+/3 width=6 by cpx_llpx_sn_conf, lift_mono, ex2_intro/ qed-.
+
+lemma cpx_lleq_conf_dx: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[h, g] T2 →
+                        ∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
+/4 width=6 by cpx_lleq_conf_sn, lleq_sym/ qed-.