- some renaming according to the written version of basic_2

[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 956ae4699a22724b2b878425a51ed28792a86be3..ee49dc20c8c9b76f3f5994c0a228c88e6b943ed9 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
@@ -19,21 +19,21 @@ 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⦄ →
+                        λR,l,T,L1,L2. |L1| = |L2| ∧
+                        (∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ →
                            ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[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
+#n #IHn #L1 #U #Hn #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
+#I1 #I2 #K1 #K2 #V1 #V2 #i #Hli #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
+| * #J1 #K10 #W10 #j #Hlj #Hji #HnU #HLK10 #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
   elim (drop_O1_lt (Ⓕ) L2 j) [2: <HL12 /2 width=5 by drop_fwd_length_lt2/ ] #J2 #K20 #W20 #HLK20
@@ -44,10 +44,10 @@ theorem llpx_sn_llpx_sn_alt: ∀R,T,L1,L2,d. llpx_sn R d T L1 L2 → llpx_sn_alt
 ]
 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
+#n #IHn #L1 #U #Hn #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/
 lapply (drop_fwd_drop2 … HLK1) #H1