support for abstract candidates of reducibility closed! ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / unfold / tpss_ltps.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_ltps.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_ltps.ma
index 18b181741955bc3c94b3082b69847ae7c082fb0b..58b63cd01ced50d02898ae3087c4d95a703d98e1 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_ltps.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_ltps.ma
@@ -20,16 +20,16 @@ include "Basic_2/unfold/tpss_tpss.ma".
 (* Properties concerning parallel substitution on local environments ********)
 
 lemma ltps_tpss_conf_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2.
-                         d1 + e1 â\89¤ d2 â\86\92 L0 [d1, e1] â\89« L1 →
-                         L0 â\8a¢ T2 [d2, e2] â\89«* U2 â\86\92 L1 â\8a¢ T2 [d2, e2] â\89«* U2.
+                         d1 + e1 â\89¤ d2 â\86\92 L0 [d1, e1] â\96¶ L1 →
+                         L0 â\8a¢ T2 [d2, e2] â\96¶* U2 â\86\92 L1 â\8a¢ T2 [d2, e2] â\96¶* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HL01 #H @(tpss_ind … H) -U2 //
 #U #U2 #_ #HU2 #IHU
 lapply (ltps_tps_conf_ge … HU2 … HL01 ?) -HU2 -HL01 // /2 width=3/
 qed.
 
 lemma ltps_tpss_conf: ∀L0,L1,T2,U2,d1,e1,d2,e2.
-                      L0 [d1, e1] â\89« L1 â\86\92 L0 â\8a¢ T2 [d2, e2] â\89«* U2 →
-                      â\88\83â\88\83T. L1 â\8a¢ T2 [d2, e2] â\89«* T & L1 â\8a¢ U2 [d1, e1] â\89«* T.
+                      L0 [d1, e1] â\96¶ L1 â\86\92 L0 â\8a¢ T2 [d2, e2] â\96¶* U2 →
+                      â\88\83â\88\83T. L1 â\8a¢ T2 [d2, e2] â\96¶* T & L1 â\8a¢ U2 [d1, e1] â\96¶* T.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #HL01 #H @(tpss_ind … H) -U2
 [ /3 width=3/
 | #U #U2 #_ #HU2 * #T #HT2 #HUT
@@ -40,16 +40,16 @@ lemma ltps_tpss_conf: ∀L0,L1,T2,U2,d1,e1,d2,e2.
 qed.
 
 lemma ltps_tpss_trans_ge: ∀L0,L1,T2,U2,d1,e1,d2,e2.
-                          d1 + e1 â\89¤ d2 â\86\92 L1 [d1, e1] â\89« L0 →
-                          L0 â\8a¢ T2 [d2, e2] â\89«* U2 â\86\92 L1 â\8a¢ T2 [d2, e2] â\89«* U2.
+                          d1 + e1 â\89¤ d2 â\86\92 L1 [d1, e1] â\96¶ L0 →
+                          L0 â\8a¢ T2 [d2, e2] â\96¶* U2 â\86\92 L1 â\8a¢ T2 [d2, e2] â\96¶* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde1d2 #HL10 #H @(tpss_ind … H) -U2 //
 #U #U2 #_ #HU2 #IHU
 lapply (ltps_tps_trans_ge … HU2 … HL10 ?) -HU2 -HL10 // /2 width=3/
 qed.
 
 lemma ltps_tpss_trans_down: ∀L0,L1,T2,U2,d1,e1,d2,e2. d2 + e2 ≤ d1 →
-                            L1 [d1, e1] â\89« L0 â\86\92 L0 â\8a¢ T2 [d2, e2] â\89«* U2 →
-                            â\88\83â\88\83T. L1 â\8a¢ T2 [d2, e2] â\89«* T & L0 â\8a¢ T [d1, e1] â\89«* U2.
+                            L1 [d1, e1] â\96¶ L0 â\86\92 L0 â\8a¢ T2 [d2, e2] â\96¶* U2 →
+                            â\88\83â\88\83T. L1 â\8a¢ T2 [d2, e2] â\96¶* T & L0 â\8a¢ T [d1, e1] â\96¶* U2.
 #L0 #L1 #T2 #U2 #d1 #e1 #d2 #e2 #Hde2d1 #HL10 #H @(tpss_ind … H) -U2
 [ /3 width=3/
 | #U #U2 #_ #HU2 * #T #HT2 #HTU
@@ -60,36 +60,36 @@ lemma ltps_tpss_trans_down: ∀L0,L1,T2,U2,d1,e1,d2,e2. d2 + e2 ≤ d1 →
 qed.
 
 fact ltps_tps_trans_eq_aux: ∀Y1,X2,L1,T2,U2,d,e.
-                            L1 â\8a¢ T2 [d, e] â\89« U2 â\86\92 â\88\80L0. L0 [d, e] â\89« L1 →
-                            Y1 = L1 â\86\92 X2 = T2 â\86\92 L0 â\8a¢ T2 [d, e] â\89«* U2.
+                            L1 â\8a¢ T2 [d, e] â\96¶ U2 â\86\92 â\88\80L0. L0 [d, e] â\96¶ L1 →
+                            Y1 = L1 â\86\92 X2 = T2 â\86\92 L0 â\8a¢ T2 [d, e] â\96¶* U2.
 #Y1 #X2 @(cw_wf_ind … Y1 X2) -Y1 -X2 #Y1 #X2 #IH
 #L1 #T2 #U2 #d #e * -L1 -T2 -U2 -d -e
 [ //
 | #L1 #K1 #V1 #W1 #i #d #e #Hdi #Hide #HLK1 #HVW1 #L0 #HL10 #H1 #H2 destruct
   lapply (ldrop_fwd_lw … HLK1) normalize #H1
-  elim (ltps_ldrop_trans_be … HL10 … HLK1 ? ?) -HL10 -HLK1 /2 width=1/ #X #H #HLK0
+  elim (ltps_ldrop_trans_be … HL10 … HLK1 ? ?) -HL10 -HLK1 // /2 width=2/ #X #H #HLK0
   elim (ltps_inv_tps22 … H ?) -H /2 width=1/ #K0 #V0 #HK01 #HV01 #H destruct
   lapply (tps_fwd_tw … HV01) #H2
   lapply (transitive_le (#[K1] + #[V0]) … H1) -H1 /2 width=1/ -H2 #H
   lapply (IH … HV01 … HK01 ? ?) -IH -HV01 -HK01
   [1,3: // |2,4: skip | normalize /2 width=1/ | /3 width=6/ ]
 | #L #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #L0 #HL0 #H1 #H2 destruct
-  lapply (tps_lsubs_conf … HT12 (L. 𝕓{I} V1) ?) -HT12 /2 width=1/ #HT12
-  lapply (IH … HV12 … HL0 ? ?) -HV12 [1,3,5: normalize // |2,4: skip ] #HV12
-  lapply (IH … HT12 (L0. 𝕓{I} V1) ? ? ?) -IH -HT12 [1,3,5: /2 width=2/ |2,4: skip | normalize // ] -HL0 #HT12
-  lapply (tpss_lsubs_conf … HT12 (L0. 𝕓{I} V2) ?) -HT12 /2 width=1/
+  lapply (tps_lsubs_conf … 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/
 | #L #I #V1 #V2 #T1 #T2 #d #e #HV12 #HT12 #L0 #HL0 #H1 #H2 destruct
-  lapply (IH … HV12 … HL0 ? ?) -HV12 [1,3,5: normalize // |2,4: skip ]
+  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/
 ]
 qed.
 
-lemma ltps_tps_trans_eq: â\88\80L1,T2,U2,d,e. L1 â\8a¢ T2 [d, e] â\89« U2 →
-                         â\88\80L0. L0 [d, e] â\89« L1 â\86\92 L0 â\8a¢ T2 [d, e] â\89«* U2.
+lemma ltps_tps_trans_eq: â\88\80L1,T2,U2,d,e. L1 â\8a¢ T2 [d, e] â\96¶ U2 →
+                         â\88\80L0. L0 [d, e] â\96¶ L1 â\86\92 L0 â\8a¢ T2 [d, e] â\96¶* U2.
 /2 width=5/ qed.
 
-lemma ltps_tpss_trans_eq: â\88\80L0,L1,T2,U2,d,e. L0 [d, e] â\89« L1 →
-                          L1 â\8a¢ T2 [d, e] â\89«* U2 â\86\92 L0 â\8a¢ T2 [d, e] â\89«* U2.
+lemma ltps_tpss_trans_eq: â\88\80L0,L1,T2,U2,d,e. L0 [d, e] â\96¶ L1 →
+                          L1 â\8a¢ T2 [d, e] â\96¶* U2 â\86\92 L0 â\8a¢ T2 [d, e] â\96¶* U2.
 #L0 #L1 #T2 #U2 #d #e #HL01 #H @(tpss_ind … H) -U2 //
 #U #U2 #_ #HU2 #IHU @(tpss_trans_eq … IHU) /2 width=3/
 qed.