minor update

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / llpx_sn_alt.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/llpx_sn_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/llpx_sn_alt.ma
index 126b733215b7d363ef1094a256172b5b9cd81657..f40046c5f7a5185da74e0fe8a92424ff1121accb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/llpx_sn_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/llpx_sn_alt.ma
@@ -19,44 +19,45 @@ include "basic_2/multiple/llpx_sn_alt_rec.ma".
 
 (* alternative definition of llpx_sn (not recursive) *)
 definition llpx_sn_alt: relation3 lenv term term → relation4 ynat term lenv lenv ≝
-                        λR,d,T,L1,L2. |L1| = |L2| ∧
-                        (∀I1,I2,K1,K2,V1,V2,i. d ≤ yinj i → L1 ⊢ i ϵ 𝐅*[d]⦃T⦄ →
-                           â\87©[i] L1 â\89¡ K1.â\93\91{I1}V1 â\86\92 â\87©[i] L2 ≡ K2.ⓑ{I2}V2 →
+                        λR,l,T,L1,L2. |L1| = |L2| ∧
+                        (∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ →
+                           â¬\87[i] L1 â\89¡ K1.â\93\91{I1}V1 â\86\92 â¬\87[i] L2 ≡ K2.ⓑ{I2}V2 →
                            I1 = I2 ∧ R K1 V1 V2
                         ).
 
 (* Main properties **********************************************************)
 
-theorem llpx_sn_llpx_sn_alt: ∀R,T,L1,L2,d. llpx_sn R d T L1 L2 → llpx_sn_alt R d T L1 L2.
+theorem llpx_sn_llpx_sn_alt: ∀R,T,L1,L2,l. llpx_sn R l T L1 L2 → llpx_sn_alt R l T L1 L2.
 #R #U #L1 @(f2_ind … rfw … L1 U) -L1 -U
-#n #IHn #L1 #U #Hn #L2 #d #H elim (llpx_sn_inv_alt_r … H) -H
+#x #IHx #L1 #U #Hx #L2 #l #H elim (llpx_sn_inv_alt_r … H) -H
 #HL12 #IHU @conj //
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hdi #H #HLK1 #HLK2 elim (frees_inv … H) -H
-[ -n #HnU elim (IHU … HnU HLK1 HLK2) -IHU -HnU -HLK1 -HLK2 /2 width=1 by conj/
-| * #J1 #K10 #W10 #j #Hdj #Hji #HnU #HLK10 #HnW10 destruct
+#I1 #I2 #K1 #K2 #V1 #V2 #i #Hli #H #HLK1 #HLK2 elim (frees_inv … H) -H
+[ -x #HnU elim (IHU … HnU HLK1 HLK2) -IHU -HnU -HLK1 -HLK2 /2 width=1 by conj/
+| * #J1 #K10 #W10 #j #Hlj #Hji #HnU #HLK10 <yminus_SO2 >yminus_inj >yminus_inj #HnW10 destruct
   lapply (drop_fwd_drop2 … HLK10) #H
-  lapply (drop_conf_ge … H … HLK1 ?) -H /2 width=1 by lt_to_le/ <minus_plus #HK10
+  lapply (drop_conf_ge … H … HLK1 ?) -H /2 width=1 by ylt_fwd_le_succ1/ <minus_plus #HK10
   elim (drop_O1_lt (Ⓕ) L2 j) [2: <HL12 /2 width=5 by drop_fwd_length_lt2/ ] #J2 #K20 #W20 #HLK20
   lapply (drop_fwd_drop2 … HLK20) #H
-  lapply (drop_conf_ge … H … HLK2 ?) -H /2 width=1 by lt_to_le/ <minus_plus #HK20
-  elim (IHn K10 W10 … K20 0) -IHn -HL12 /3 width=6 by drop_fwd_rfw/
-  elim (IHU … HnU HLK10 HLK20) -IHU -HnU -HLK10 -HLK20 //
+  lapply (drop_conf_ge … H … HLK2 ?) -H /2 width=1 by ylt_fwd_le_succ1/ <minus_plus #HK20
+  elim (IHx K10 W10 … K20 0 ?) -IHx -HL12 /3 width=6 by drop_fwd_rfw/
+  elim (IHU … HnU HLK10 HLK20) -IHU -HnU -HLK10 -HLK20 /2 width=6 by/
 ]
 qed.
 
-theorem llpx_sn_alt_inv_llpx_sn: ∀R,T,L1,L2,d. llpx_sn_alt R d T L1 L2 → llpx_sn R d T L1 L2.
+theorem llpx_sn_alt_inv_llpx_sn: ∀R,T,L1,L2,l. llpx_sn_alt R l T L1 L2 → llpx_sn R l T L1 L2.
 #R #U #L1 @(f2_ind … rfw … L1 U) -L1 -U
-#n #IHn #L1 #U #Hn #L2 #d * #HL12 #IHU @llpx_sn_intro_alt_r //
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hdi #HnU #HLK1 #HLK2 destruct
+#x #IHx #L1 #U #Hx #L2 #l * #HL12 #IHU @llpx_sn_intro_alt_r //
+#I1 #I2 #K1 #K2 #V1 #V2 #i #Hli #HnU #HLK1 #HLK2 destruct
 elim (IHU … HLK1 HLK2) /3 width=2 by frees_eq/
-#H #HV12 @and3_intro // @IHn -IHn /3 width=6 by drop_fwd_rfw/
+#H #HV12 @and3_intro // @IHx -IHx /3 width=6 by drop_fwd_rfw/
 lapply (drop_fwd_drop2 … HLK1) #H1
 lapply (drop_fwd_drop2 … HLK2) -HLK2 #H2
 @conj [ @(drop_fwd_length_eq1 … H1 H2) // ] -HL12
 #Z1 #Z2 #Y1 #Y2 #X1 #X2 #j #_
 >(minus_plus_m_m j (i+1)) in ⊢ (%→?); >commutative_plus <minus_plus
+<yminus_inj <yminus_inj >yminus_SO2 
 #HnV1 #HKY1 #HKY2 (**) (* full auto too slow *)
 lapply (drop_trans_ge … H1 … HKY1 ?) -H1 -HKY1 // #HLY1
 lapply (drop_trans_ge … H2 … HKY2 ?) -H2 -HKY2 // #HLY2
-/4 width=14 by frees_be, yle_plus_dx2_trans, yle_succ_dx/
+/4 width=9 by frees_be, yle_plus_dx2_trans, yle_succ_dx, ylt_inj/
 qed-.