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[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / unfold / ltpss_ltpss.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_ltpss.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_ltpss.ma
index cb8b981c675d981a31762574be571c8dfeaf5f73..f866adc126cd41eb357b208098568ee8a483a81c 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_ltpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_ltpss.ma
@@ -49,20 +49,20 @@ fact ltpss_tpss_trans_eq_aux: ∀Y1,X2,L1,T2,U2,d,e.
 #Y1 #X2 @(cw_wf_ind … Y1 X2) -Y1 -X2 #Y1 #X2 #IH
 #L1 #T2 #U2 #d #e #H @(tpss_ind_alt … H) -L1 -T2 -U2 -d -e
 [ //
-| #L1 #K1 #V1 #V2 #W2 #i #d #e #Hdi #Hide #HLK1 #HV12 #HVW2 #_ #L0 #HL10 #H1 #H2 destruct
+| #L1 #K1 #V1 #V2 #W2 #i #d #e #Hdi #Hide #HLK1 #HV12 #HVW2 #_ #L0 #HL01 #H1 #H2 destruct
   lapply (ldrop_fwd_lw … HLK1) #H1 normalize in H1;
-  elim (ltpss_ldrop_trans_be … HL10 … HLK1 ? ?) -HL10 -HLK1 // /2 width=2/ #X #H #HLK0
+  elim (ltpss_ldrop_trans_be … HL01 … HLK1 ? ?) -HL01 -HLK1 // /2 width=2/ #X #H #HLK0
   elim (ltpss_inv_tpss22 … H ?) -H /2 width=1/ #K0 #V0 #HK01 #HV01 #H destruct
   lapply (tpss_fwd_tw … HV01) #H2
-  lapply (transitive_le (#[K1] + #[V0]) … H1) -H1 /2 width=1/ -H2 #H
+  lapply (transitive_le (#{K1} + #{V0}) … H1) -H1 /2 width=1/ -H2 #H
   lapply (tpss_trans_eq … HV01 HV12) -V1 #HV02
   lapply (IH … HV02 … HK01 ? ?) -IH -HV02 -HK01
   [1,3: // |2,4: skip | normalize /2 width=1/ | /2 width=6/ ]
-| #L #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #_ #_ #L0 #HL0 #H1 #H2 destruct
-  lapply (tpss_lsubs_conf … HT12 (L. ⓑ{I} V1) ?) -HT12 /2 width=1/ #HT12
+| #L #a #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #_ #_ #L0 #HL0 #H1 #H2 destruct
+  lapply (tpss_lsubs_trans … HT12 (L. ⓑ{I} V1) ?) -HT12 /2 width=1/ #HT12
   lapply (IH … HV12 … HL0 ? ?) -HV12 [1,3: // |2,4: skip |5: /2 width=2/ ] #HV12
   lapply (IH … HT12 (L0. ⓑ{I} V1) ? ? ?) -IH -HT12 [1,3,5: /2 width=2/ |2,4: skip | normalize // ] -HL0 #HT12
-  lapply (tpss_lsubs_conf … HT12 (L0. ⓑ{I} V2) ?) -HT12 /2 width=1/
+  lapply (tpss_lsubs_trans … HT12 (L0. ⓑ{I} V2) ?) -HT12 /2 width=1/
 | #L #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #_ #_ #L0 #HL0 #H1 #H2 destruct
   lapply (IH … HV12 … HL0 ? ?) -HV12 [1,3: // |2,4: skip |5: /2 width=3/ ]
   lapply (IH … HT12 … HL0 ? ?) -IH -HT12 [1,3,5: normalize // |2,4: skip ] -HL0 /2 width=1/
@@ -133,3 +133,14 @@ lemma ltpss_conf: ∀L0,L1,d1,e1. L0 ▶* [d1, e1] L1 →
                   ∀L2,d2,e2. L0 ▶* [d2, e2] L2 →
                   ∃∃L. L1 ▶* [d2, e2] L & L2 ▶* [d1, e1] L.
 /2 width=7/ qed.
+
+theorem ltpss_trans_eq: ∀L1,L,d,e. L1 ▶* [d, e] L →
+                        ∀L2. L ▶* [d, e] L2 → L1 ▶* [d, e] L2.
+#L1 #L #d #e #H elim H -L1 -L -d -e //
+[ #L1 #L #I #V1 #V #e #_ #HV1 #IHL1 #X #H
+  elim (ltpss_inv_tpss21 … H ?) -H // <minus_plus_m_m #L2 #V2 #HL2 #HV2 #H destruct
+  elim (ltpss_tpss_conf … HV1 … HL2) -HV1 #V0 #HV10 #HV0
+  elim (tpss_conf_eq … HV2 … HV0) -V #V #HV2 #HV0
+  lapply (tpss_trans_eq … HV10 … HV0) -V0 #HV1
+  @ltpss_tpss2 /2 width=1/
+        
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