- lambda_delta: we updated some notation

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_tpss.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_tpss.ma
index 2b1b8377c2f5c128f871e87917b1a9eeb2a7872c..f071019f8e42e63f5eff1fc5fca480c7d9bb35b5 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_tpss.ma
@@ -19,19 +19,19 @@ include "basic_2/unfold/ltpss_tps.ma".
 
 (* Properties concerning partial unfold on terms ****************************)
 
-lemma ltpss_tpss_conf_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶* U2 →
-                          ∀L1,d1,e1. L0 [d1, e1] ▶* L1 → d1 + e1 ≤ d2 →
-                          L1 ⊢ T2 [d2, e2] ▶* U2.
+lemma ltpss_tpss_conf_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 ▶* [d2, e2] U2 →
+                          ∀L1,d1,e1. L0 ▶* [d1, e1] L1 → d1 + e1 ≤ d2 →
+                          L1 ⊢ T2 ▶* [d2, e2] U2.
 #L0 #T2 #U2 #d2 #e2 #H #L1 #d1 #e1 #HL01 #Hde1d2 @(tpss_ind … H) -U2 //
 #U #U2 #_ #HU2 #IHU
 lapply (ltpss_tps_conf_ge … HU2 … HL01 ?) -L0 // -Hde1d2 /2 width=3/
 qed.
 
 (* Basic_1: was: subst1_subst1_back *)
-lemma ltpss_tps_conf: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
-                      ∀L1,d1,e1. L0 [d1, e1] ▶* L1 →
-                      ∃∃T. L1 ⊢ T2 [d2, e2] ▶ T &
-                           L1 ⊢ U2 [d1, e1] ▶* T.
+lemma ltpss_tps_conf: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 ▶ [d2, e2] U2 →
+                      ∀L1,d1,e1. L0 ▶* [d1, e1] L1 →
+                      ∃∃T. L1 ⊢ T2 ▶ [d2, e2] T &
+                           L1 ⊢ U2 ▶* [d1, e1] T.
 #L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
 [ /2 width=3/
 | #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL01
@@ -51,7 +51,7 @@ lemma ltpss_tps_conf: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
     | lapply (ltpss_ldrop_conf_ge … HL01 … HLK0 ?) -L0 // /3 width=4/
     ]
   ]
-| #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL01
+| #L0 #a #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL01
   elim (IHVW2 … HL01) -IHVW2 #V #HV2 #HVW2
   elim (IHTU2 (L1. ⓑ{I} V) (d1 + 1) e1 ?) -IHTU2 /2 width=1/ -HL01 /3 width=5/
 | #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL01
@@ -60,19 +60,19 @@ lemma ltpss_tps_conf: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
 ]
 qed.
   
-lemma ltpss_tpss_trans_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶* U2 →
-                           ∀L1,d1,e1. L1 [d1, e1] ▶* L0 → d1 + e1 ≤ d2 →
-                           L1 ⊢ T2 [d2, e2] ▶* U2.
+lemma ltpss_tpss_trans_ge: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 ▶* [d2, e2] U2 →
+                           ∀L1,d1,e1. L1 ▶* [d1, e1] L0 → d1 + e1 ≤ d2 →
+                           L1 ⊢ T2 ▶* [d2, e2] U2.
 #L0 #T2 #U2 #d2 #e2 #H #L1 #d1 #e1 #HL01 #Hde1d2 @(tpss_ind … H) -U2 //
 #U #U2 #_ #HU2 #IHU
 lapply (ltpss_tps_trans_ge … HU2 … HL01 ?) -L0 // -Hde1d2 /2 width=3/
 qed.
 
 (* Basic_1: was: subst1_subst1 *)
-lemma ltpss_tps_trans: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
-                       ∀L1,d1,e1. L1 [d1, e1] ▶* L0 →
-                       ∃∃T. L1 ⊢ T2 [d2, e2] ▶ T &
-                            L0 ⊢ T [d1, e1] ▶* U2.
+lemma ltpss_tps_trans: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 ▶ [d2, e2] U2 →
+                       ∀L1,d1,e1. L1 ▶* [d1, e1] L0 →
+                       ∃∃T. L1 ⊢ T2 ▶ [d2, e2] T &
+                            L0 ⊢ T ▶* [d1, e1] U2.
 #L0 #T2 #U2 #d2 #e2 #H elim H -L0 -T2 -U2 -d2 -e2
 [ /2 width=3/
 | #L0 #K0 #V0 #W0 #i2 #d2 #e2 #Hdi2 #Hide2 #HLK0 #HVW0 #L1 #d1 #e1 #HL10
@@ -92,7 +92,7 @@ lemma ltpss_tps_trans: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
     | lapply (ltpss_ldrop_trans_ge … HL10 … HLK0 ?) -HL10 -HLK0 // /3 width=4/
     ]
   ]
-| #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL10
+| #L0 #a #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL10
   elim (IHVW2 … HL10) -IHVW2 #V #HV2 #HVW2
   elim (IHTU2 (L1. ⓑ{I} V) (d1 + 1) e1 ?) -IHTU2 /2 width=1/ -HL10 /3 width=5/
 | #L0 #I #V2 #W2 #T2 #U2 #d2 #e2 #_ #_ #IHVW2 #IHTU2 #L1 #d1 #e1 #HL10
@@ -100,39 +100,3 @@ lemma ltpss_tps_trans: ∀L0,T2,U2,d2,e2. L0 ⊢ T2 [d2, e2] ▶ U2 →
   elim (IHTU2 … HL10) -IHTU2 -HL10 /3 width=5/
 ]
 qed.
-
-fact ltpss_tps_trans_eq_aux: ∀Y1,X2,L1,T2,U2,d,e.
-                             L1 ⊢ T2 [d, e] ▶ U2 → ∀L0. L0 [d, e] ▶* L1 →
-                             Y1 = L1 → X2 = T2 → L0 ⊢ T2 [d, e] ▶* 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) #H1 normalize in H1;
-  elim (ltpss_ldrop_trans_be … HL10 … HLK1 ? ?) -HL10 -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 (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. ⓑ{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: // |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: ∀L1,T2,U2,d,e. L1 ⊢ T2 [d, e] ▶ U2 →
-                         ∀L0. L0 [d, e] ▶ L1 → L0 ⊢ T2 [d, e] ▶* U2.
-/2 width=5/ qed.
-
-lemma ltps_tpss_trans_eq: ∀L0,L1,T2,U2,d,e. L0 [d, e] ▶ L1 →
-                          L1 ⊢ T2 [d, e] ▶* U2 → L0 ⊢ T2 [d, e] ▶* 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.
-*)