update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reducibility / ltpr_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reducibility/ltpr_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/reducibility/ltpr_aaa.ma
index b45dbb99eb2fe5333ed2c773f9d911ad90d5a5e7..5208a64051ca975c82ac18093e100044aa2bc91b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reducibility/ltpr_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reducibility/ltpr_aaa.ma
@@ -20,52 +20,55 @@ 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.
-#L #T @(fw_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
+lemma aaa_ltpr_tpr_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2. L1 ➡ L2 →
+                         ∀T2. T1 ➡ T2 → L2 ⊢ T2 ⁝ A.
+#L1 #T1 @(f2_ind … fw … L1 T1) -L1 -T1 #n #IH #L1 * *
+[1,2,3:
+  #i #Hn #X #H1 #L2 #HL12 #Y #H2 destruct
+  >(tpr_inv_atom1 … H2) -Y
+|4,5: [ #a ] * #V1 #T1 #Hn #X #H1 #L2 #HL12 #Y #H2 destruct
+]
+[ >(aaa_inv_sort … H1) -X //
+| elim (aaa_inv_lref … H1) #I #K1 #V1 #HLK1 #HA
   lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) #HKV1
-  elim (ltpr_ldrop_conf … HLK1 … HL12) -HLK1 -HL12 #X #H #HLK2
+  elim (ltpr_ldrop_conf … HLK1 … HL12) -HLK1 -HL12 #Y #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/
-| #a #L1 #V1 #T1 #B #A #HB #HA #H1 #H2 #L2 #HL12 #X #H destruct
-  elim (tpr_inv_abbr1 … H) -H *
+  lapply (IH … HKV1 … HA … HK12 … HV12) -L1 -K1 -V1 /2 width=5/
+| elim (aaa_inv_gref … H1)
+| elim (aaa_inv_abbr … H1) -H1 #B #HB #HA
+  elim (tpr_inv_abbr1 … H2) -H2 *
   [ #V2 #T #T2 #HV12 #HT1 #HT2 #H destruct
-    lapply (tps_lsubs_trans … HT2 (L2.ⓓV2) ?) -HT2 /2 width=1/ #HT2
+    lapply (tps_lsubr_trans … HT2 (L2.ⓓV2) ?) -HT2 /2 width=1/ #HT2
     lapply (IH … HB … HL12 … HV12) -HB /width=5/ #HB
     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/
   ]
-| #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
+| elim (aaa_inv_abst … H1) -H1 #B #A #HB #HA #H destruct
+  elim (tpr_inv_abst1 … H2) -H2 #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/
-| #L1 #V1 #T1 #B #A #HV1 #HT1 #H1 #H2 #L2 #HL12 #X #H destruct
-  elim (tpr_inv_appl1 … H) -H *
+| elim (aaa_inv_appl … H1) -H1 #B #HB #HA
+  elim (tpr_inv_appl1 … H2) -H2 *
   [ #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/
-  | #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 … HB … HL12 … HV12) -HB -HV12 /width=5/ #HB
+    lapply (IH … HA … HL12 … HT12) -IH -HA -HL12 -HT12 /width=5/ /2 width=3/
+  | #b #V2 #W2 #T0 #T2 #HV12 #HT02 #H1 #H2 destruct
+    elim (aaa_inv_abst … HA) -HA #B0 #A0 #HB0 #HA0 #H destruct
+    lapply (IH … HB … HL12 … HV12) -HB -HV12 /width=5/ #HB
     lapply (IH … HB0  … HL12 W2 ?) -HB0 /width=5/ #HB0
-    lapply (IH … HA0 … (L2.ⓛW2) … HT02) -IH -HA0 -HT02 [2,4: // |3,5: skip ] /2 width=1/ -T0 -L1 -V1 /4 width=7/
-  | #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 … HA0 … (L2.ⓛW2) … HT02) -IH -HA0 -HT02 // /2 width=1/ -T0 -L1 -V1 /4 width=7/
+  | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HW02 #HT02 #HV02 #H1 #H2 destruct
+    elim (aaa_inv_abbr … HA) -HA #B0 #HW0 #HT0
     lapply (IH … HW0  … HL12 … HW02) -HW0 /width=5/ #HW2
-    lapply (IH … HV1 … HL12 … HV10) -HV1 -HV10 /width=5/ #HV0
-    lapply (IH … HT0 … (L2.ⓓW2) … HT02) -IH -HT0 -HT02 [2,4: // |3,5: skip ] /2 width=1/ -V1 -T0 -L1 -W0 #HT2
+    lapply (IH … HB … HL12 … HV10) -HB -HV10 /width=5/ #HV0
+    lapply (IH … HT0 … (L2.ⓓW2) … HT02) -IH -HT0 -HT02 // /2 width=1/ -V1 -T0 -L1 -W0 #HT2
     @(aaa_abbr … HW2) -HW2
     @(aaa_appl … HT2) -HT2 /3 width=7/ (**) (* explict constructors, /5 width=7/ is too slow *)
   ]
-| #L1 #V1 #T1 #A #HV1 #HT1 #H1 #H2 #L2 #HL12 #X #H destruct
-  elim (tpr_inv_cast1 … H) -H
+| elim (aaa_inv_cast … H1) -H1 #HV1 #HT1
+  elim (tpr_inv_cast1 … H2) -H2
   [ * #V2 #T2 #HV12 #HT12 #H destruct
     lapply (IH … HV1 … HL12 … HV12) -HV1 -HV12 /width=5/ #HV2
     lapply (IH … HT1 … HL12 … HT12) -IH -HT1 -HL12 -HT12 /width=5/ -L1 -V1 -T1 /2 width=1/
@@ -75,10 +78,6 @@ fact aaa_ltpr_tpr_conf_aux: ∀L,T,L1,T1,A. L1 ⊢ T1 ⁝ A → L = L1 → T = T
 ]
 qed.
 
-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.
 /2 width=5/ qed.