X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Freduction%2Flpx_aaa.ma;h=f9c2374c25dce8d8dc11dd08c4db3dc584f6d56a;hb=598a5c56535a8339f6533227ab580aff64e2d41c;hp=3537c8d01af5e424142f2d4f4e303ef499d3582a;hpb=e5378812c068074f0ac627541d3f066e135c8824;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma
index 3537c8d01..f9c2374c2 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpx_aaa.ma
@@ -31,39 +31,41 @@ lemma aaa_cpx_lpx_conf: ∀h,g,G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A →
   elim (cpx_inv_lref1 … H) -H
   [ #H destruct
     elim (lpx_ldrop_conf … HLK1 … HL12) -L1 #X #H #HLK2
-    elim (lpx_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct /3 width=6/
+    elim (lpx_inv_pair1 … H) -H
+    #K2 #V2 #HK12 #HV12 #H destruct /3 width=6 by aaa_lref/
   | * #J #Y #Z #V2 #H #HV12 #HV2
     lapply (ldrop_mono … H … HLK1) -H #H destruct
     elim (lpx_ldrop_conf … HLK1 … HL12) -L1 #Z #H #HLK2
     elim (lpx_inv_pair1 … H) -H #K2 #V0 #HK12 #_ #H destruct
-    lapply (ldrop_fwd_drop2 … HLK2) -V0 /3 width=7/
+    /3 width=8 by aaa_lift, ldrop_fwd_drop2/
   ]
 | #a #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
   elim (cpx_inv_abbr1 … H) -H *
-  [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=2/
+  [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=2 by lpx_pair, aaa_abbr/
   | #T2 #HT12 #HT2 #H destruct -IHV1
-    @(aaa_inv_lift … (L2.ⓓV1) … HT2) -HT2 /2 width=1/ /3 width=1/
+    /4 width=8 by lpx_pair, aaa_inv_lift, ldrop_drop/
   ]
 | #a #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
-  elim (cpx_inv_abst1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=1/
+  elim (cpx_inv_abst1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
+  /4 width=1 by lpx_pair, aaa_abst/
 | #G #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
   elim (cpx_inv_appl1 … H) -H *
-  [ #V2 #T2 #HV12 #HT12 #H destruct /3 width=3/
+  [ #V2 #T2 #HV12 #HT12 #H destruct /3 width=3 by aaa_appl/
   | #b #V2 #W1 #W2 #U1 #U2 #HV12 #HW12 #HU12 #H1 #H2 destruct
     lapply (IHV1 … HV12 … HL12) -IHV1 -HV12 #HV2
-    lapply (IHT1 (ⓛ{b}W2.U2) … HL12) -IHT1 /2 width=1/ -L1 #H
+    lapply (IHT1 (ⓛ{b}W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
     elim (aaa_inv_abst … H) -H #B0 #A0 #HW1 #HU2 #H destruct
-    lapply (lsuba_aaa_trans … HU2 (L2.ⓓⓝW2.V2) ?) -HU2 /3 width=3/
+    /5 width=6 by lsuba_aaa_trans, lsuba_abbr, aaa_abbr, aaa_cast/
   | #b #V #V2 #W1 #W2 #U1 #U2 #HV1 #HV2 #HW12 #HU12 #H1 #H2 destruct
-    lapply (aaa_lift G L2 … B … (L2.ⓓW2) … HV2) -HV2 /2 width=1/ #HV2
-    lapply (IHT1 (ⓓ{b}W2.U2) … HL12) -IHT1 /2 width=1/ -L1 #H
-    elim (aaa_inv_abbr … H) -H /3 width=3/
+    lapply (aaa_lift G L2 … B … (L2.ⓓW2) … HV2) -HV2 /2 width=2 by ldrop_drop/ #HV2
+    lapply (IHT1 (ⓓ{b}W2.U2) … HL12) -IHT1 /2 width=1 by cpx_bind/ -L1 #H
+    elim (aaa_inv_abbr … H) -H /3 width=3 by aaa_abbr, aaa_appl/
   ]
 | #G #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #X #H #L2 #HL12
   elim (cpx_inv_cast1 … H) -H
-  [ * #V2 #T2 #HV12 #HT12 #H destruct /3 width=1/
-  | -IHV1 /2 width=1/
-  | -IHT1 /2 width=1/
+  [ * #V2 #T2 #HV12 #HT12 #H destruct /3 width=1 by aaa_cast/
+  | -IHV1 /2 width=1 by/
+  | -IHT1 /2 width=1 by/
   ]
 ]
 qed-.