- the trace is explicit in all auto tactics with depth > 1

[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 ee49dc20c8c9b76f3f5994c0a228c88e6b943ed9..a849ade55611f8a9482497f1a5bba35921db05bb 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
@@ -29,27 +29,27 @@ definition llpx_sn_alt: relation3 lenv term term → relation4 ynat term lenv le
 
 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 #l #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 #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/
+[ -x #HnU elim (IHU … HnU HLK1 HLK2) -IHU -HnU -HLK1 -HLK2 /2 width=1 by conj/
 | * #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
   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 (IHx K10 W10 … K20 0) -IHx -HL12 /3 width=6 by drop_fwd_rfw/
   elim (IHU … HnU HLK10 HLK20) -IHU -HnU -HLK10 -HLK20 //
 ]
 qed.
 
 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 #l * #HL12 #IHU @llpx_sn_intro_alt_r //
+#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