X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Freducibility%2Fltpr_aaa.ma;h=ef63ad095d6468eadd660da10e5ce28a493c37ce;hb=cc21d0caa6229b7d1a905f9b62de2af4f40cc863;hp=baf1abb09e9cc5236d4f2dfb434d20ca58b48461;hpb=b8a7401daf0637a4ce8f86e960b180cb5f22ecb3;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_aaa.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_aaa.ma
index baf1abb09..ef63ad095 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_aaa.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/ltpr_aaa.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/aaa_ltps.ma".
+include "basic_2/static/aaa_ltpss_dx.ma".
 include "basic_2/static/lsuba_aaa.ma".
 include "basic_2/reducibility/ltpr_ldrop.ma".
 
@@ -20,31 +20,29 @@ include "basic_2/reducibility/ltpr_ldrop.ma".
 
 (* Properties about atomic arity assignment on terms ************************)
 
-fact aaa_ltpr_tpr_conf_aux: ∀L,T,L1,T1,A. L1 ⊢ T1 ÷ A → L = L1 → T = T1 →
-                            ∀L2. L1 ➡ L2 → ∀T2. T1 ➡ T2 → L2 ⊢ T2 ÷ A.
+fact aaa_ltpr_tpr_conf_aux: ∀L,T,L1,T1,A. L1 ⊢ T1 ⁝ A → L = L1 → T = T1 →
+                            ∀L2. L1 ➡ L2 → ∀T2. T1 ➡ T2 → L2 ⊢ T2 ⁝ A.
 #L #T @(cw_wf_ind … L T) -L -T #L #T #IH
 #L1 #T1 #A * -L1 -T1 -A
 [ -IH #L1 #k #H1 #H2 #L2 #_ #T2 #H destruct
   >(tpr_inv_atom1 … H) -H //
 | #I #L1 #K1 #V1 #B #i #HLK1 #HK1 #H1 #H2 #L2 #HL12 #T2 #H destruct
   >(tpr_inv_atom1 … H) -T2
-  lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) #HKV1
-  elim (ltpr_ldrop_conf … HLK1 … HL12) -HLK1 -HL12 #X #HLK2 #H
+  lapply (ldrop_pair2_fwd_cw … HLK1 (#i)) #HKV1
+  elim (ltpr_ldrop_conf … HLK1 … HL12) -HLK1 -HL12 #X #H #HLK2
   elim (ltpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct
   lapply (IH … HKV1 … HK1 … HK12 … HV12) // -L1 -K1 -V1 /2 width=5/
-| #L1 #V1 #T1 #B #A #HB #HA #H1 #H2 #L2 #HL12 #X #H destruct
+| #a #L1 #V1 #T1 #B #A #HB #HA #H1 #H2 #L2 #HL12 #X #H destruct
   elim (tpr_inv_abbr1 … H) -H *
-  [ #V2 #T0 #T2 #HV12 #HT10 #HT02 #H destruct
-    lapply (tps_lsubs_conf … HT02 (L2.ⓓV2) ?) -HT02 /2 width=1/ #HT02
+  [ #V2 #T #T2 #HV12 #HT1 #HT2 #H destruct
+    lapply (tps_lsubs_trans … HT2 (L2.ⓓV2) ?) -HT2 /2 width=1/ #HT2
     lapply (IH … HB … HL12 … HV12) -HB /width=5/ #HB
-    lapply (IH … HA … (L2.ⓓV2) … HT10) -IH -HA -HT10 /width=5/ -T1 /2 width=1/ -L1 -V1 /3 width=5/
-  | -B #T #HT1 #HTX
-    elim (lift_total X 0 1) #X1 #HX1
-    lapply (tpr_lift … HTX … HT1 … HX1) -T #HTX1
-    lapply (IH … HA … (L2.ⓓV1) … HTX1) /width=5/ -T1 /2 width=1/ -L1 #HA
-    @(aaa_inv_lift … HA … HX1) /2 width=1/
+    lapply (IH … HA … (L2.ⓓV2) … HT1) -IH -HA -HT1 /width=5/ -T1 /2 width=1/ -L1 -V1 /3 width=5/
+  | -B #T #HT1 #HXT #H destruct
+    lapply (IH … HA … (L2.ⓓV1) … HT1) /width=5/ -T1 /2 width=1/ -L1 #HA
+    @(aaa_inv_lift … HA … HXT) /2 width=1/
   ]
-| #L1 #V1 #T1 #B #A #HB #HA #H1 #H2 #L2 #HL12 #X #H destruct
+| #a #L1 #V1 #T1 #B #A #HB #HA #H1 #H2 #L2 #HL12 #X #H destruct
   elim (tpr_inv_abst1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
   lapply (IH … HB … HL12 … HV12) -HB /width=5/ #HB
   lapply (IH … HA … (L2.ⓛV2) … HT12) -IH -HA -HT12 /width=5/ -T1 /2 width=1/
@@ -53,12 +51,12 @@ fact aaa_ltpr_tpr_conf_aux: ∀L,T,L1,T1,A. L1 ⊢ T1 ÷ A → L = L1 → T = T1
   [ #V2 #T2 #HV12 #HT12 #H destruct
     lapply (IH … HV1 … HL12 … HV12) -HV1 -HV12 /width=5/ #HB
     lapply (IH … HT1 … HL12 … HT12) -IH -HT1 -HL12 -HT12 /width=5/ /2 width=3/
-  | #V2 #W2 #T0 #T2 #HV12 #HT02 #H1 #H2 destruct
+  | #a #V2 #W2 #T0 #T2 #HV12 #HT02 #H1 #H2 destruct
     elim (aaa_inv_abst … HT1) -HT1 #B0 #A0 #HB0 #HA0 #H destruct
     lapply (IH … HV1 … HL12 … HV12) -HV1 -HV12 /width=5/ #HB
     lapply (IH … HB0  … HL12 W2 ?) -HB0 /width=5/ #HB0
     lapply (IH … HA0 … (L2.ⓛW2) … HT02) -IH -HA0 -HT02 /width=5/ -T0 /2 width=1/ -L1 -V1 /4 width=7/
-  | #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HW02 #HT02 #HV02 #H1 #H2 destruct
+  | #a #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HW02 #HT02 #HV02 #H1 #H2 destruct
     elim (aaa_inv_abbr … HT1) -HT1 #B0 #HW0 #HT0
     lapply (IH … HW0  … HL12 … HW02) -HW0 /width=5/ #HW2
     lapply (IH … HV1 … HL12 … HV10) -HV1 -HV10 /width=5/ #HV0
@@ -77,12 +75,12 @@ fact aaa_ltpr_tpr_conf_aux: ∀L,T,L1,T1,A. L1 ⊢ T1 ÷ A → L = L1 → T = T1
 ]
 qed.
 
-lemma aaa_ltpr_tpr_conf: ∀L1,T1,A. L1 ⊢ T1 ÷ A → ∀L2. L1 ➡ L2 →
-                         ∀T2. T1 ➡ T2 → L2 ⊢ T2 ÷ A.
+lemma aaa_ltpr_tpr_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2. L1 ➡ L2 →
+                         ∀T2. T1 ➡ T2 → L2 ⊢ T2 ⁝ A.
 /2 width=9/ qed.
 
-lemma aaa_ltpr_conf: ∀L1,T,A. L1 ⊢ T ÷ A → ∀L2. L1 ➡ L2 → L2 ⊢ T ÷ A.
+lemma aaa_ltpr_conf: ∀L1,T,A. L1 ⊢ T ⁝ A → ∀L2. L1 ➡ L2 → L2 ⊢ T ⁝ A.
 /2 width=5/ qed.
 
-lemma aaa_tpr_conf: ∀L,T1,A. L ⊢ T1 ÷ A → ∀T2. T1 ➡ T2 → L ⊢ T2 ÷ A.
+lemma aaa_tpr_conf: ∀L,T1,A. L ⊢ T1 ⁝ A → ∀T2. T1 ➡ T2 → L ⊢ T2 ⁝ A.
 /2 width=5/ qed.