X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2Fbasic_2%2Funfold%2Fltpss_ldrop.ma;h=8787d594ef82931cb82d5c0749504be29c13d0f6;hb=fde3b3d2e6cc48f6c9880136b1a0d565e2c78c1f;hp=b52cedae7698c826d1f7770b99574a408e9f5a50;hpb=eb918fc784eacd2094e3986ba321ef47690d9983;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_ldrop.ma b/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_ldrop.ma
index b52cedae7..8787d594e 100644
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_ldrop.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/ltpss_ldrop.ma
@@ -12,63 +12,120 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/substitution/ltps_ldrop.ma".
-include "Basic_2/unfold/ltpss.ma".
+include "basic_2/unfold/ltpss.ma".
 
-(* PARTIAL UNFOLD ON LOCAL ENVIRONMENTS *************************************)
+(* PARALLEL UNFOLD ON LOCAL ENVIRONMENTS ************************************)
 
-lemma ltpss_ldrop_conf_ge: ∀L0,L1,d1,e1. L0 [d1, e1] ▶* L1 →
+lemma ltpss_ldrop_conf_ge: ∀L0,L1,d1,e1. L0 ▶* [d1, e1] L1 →
                            ∀L2,e2. ⇩[0, e2] L0 ≡ L2 →
                            d1 + e1 ≤ e2 → ⇩[0, e2] L1 ≡ L2.
-#L0 #L1 #d1 #e1 #H @(ltpss_ind … H) -L1 // /3 width=6/
+#L0 #L1 #d1 #e1 #H elim H -L0 -L1 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H //
+| //
+| normalize #K0 #K1 #I #V0 #V1 #e1 #_ #_ #IHK01 #L2 #e2 #H #He12
+  elim (le_inv_plus_l … He12) #_ #He2
+  lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
+  lapply (IHK01 … HK0L2 ?) -K0 /2 width=1/
+| #K0 #K1 #I #V0 #V1 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHK01 #L2 #e2 #H #Hd1e2
+  elim (le_inv_plus_l … Hd1e2) #_ #He2
+  lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
+  lapply (IHK01 … HK0L2 ?) -K0 /2 width=1/
+]
 qed.
 
-lemma ltpss_ldrop_trans_ge: ∀L1,L0,d1,e1. L1 [d1, e1] ▶* L0 →
+lemma ltpss_ldrop_trans_ge: ∀L1,L0,d1,e1. L1 ▶* [d1, e1] L0 →
                             ∀L2,e2. ⇩[0, e2] L0 ≡ L2 →
                             d1 + e1 ≤ e2 → ⇩[0, e2] L1 ≡ L2.
-#L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0 // /3 width=6/
+#L1 #L0 #d1 #e1 #H elim H -L1 -L0 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H //
+| //
+| normalize #K1 #K0 #I #V1 #V0 #e1 #_ #_ #IHK10 #L2 #e2 #H #He12
+  elim (le_inv_plus_l … He12) #_ #He2
+  lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
+  lapply (IHK10 … HK0L2 ?) -K0 /2 width=1/
+| #K0 #K1 #I #V1 #V0 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHK10 #L2 #e2 #H #Hd1e2
+  elim (le_inv_plus_l … Hd1e2) #_ #He2
+  lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
+  lapply (IHK10 … HK0L2 ?) -IHK10 -HK0L2 /2 width=1/
+]
 qed.
 
-lemma ltpss_ldrop_conf_be: ∀L0,L1,d1,e1. L0 [d1, e1] ▶* L1 →
+lemma ltpss_ldrop_conf_be: ∀L0,L1,d1,e1. L0 ▶* [d1, e1] L1 →
                            ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 →
-                           ∃∃L. L2 [0, d1 + e1 - e2] ▶* L & ⇩[0, e2] L1 ≡ L.
-#L0 #L1 #d1 #e1 #H @(ltpss_ind … H) -L1
-[ /2 width=3/
-| #L #L1 #_ #HL1 #IHL #L2 #e2 #HL02 #Hd1e2 #He2de1
-  elim (IHL … HL02 Hd1e2 He2de1) -L0 #L0 #HL20 #HL0
-  elim (ltps_ldrop_conf_be … HL1 … HL0 Hd1e2 He2de1) -L /3 width=3/
+                           ∃∃L. L2 ▶* [0, d1 + e1 - e2] L & ⇩[0, e2] L1 ≡ L.
+#L0 #L1 #d1 #e1 #H elim H -L0 -L1 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/
+| normalize #L #I #V #L2 #e2 #HL2 #_ #He2
+  lapply (le_n_O_to_eq … He2) -He2 #H destruct
+  lapply (ldrop_inv_refl … HL2) -HL2 #H destruct /2 width=3/
+| normalize #K0 #K1 #I #V0 #V1 #e1 #HK01 #HV01 #IHK01 #L2 #e2 #H #_ #He21
+  lapply (ldrop_inv_O1 … H) -H * * #He2 #HK0L2
+  [ -IHK01 -He21 destruct <minus_n_O /3 width=3/
+  | -HK01 -HV01 <minus_le_minus_minus_comm //
+    elim (IHK01 … HK0L2 ? ?) -K0 // /2 width=1/ /3 width=3/
+  ]
+| #K0 #K1 #I #V0 #V1 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHK01 #L2 #e2 #H #Hd1e2 #He2de1
+  elim (le_inv_plus_l … Hd1e2) #_ #He2
+  <minus_le_minus_minus_comm //
+  lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
+  elim (IHK01 … HK0L2 ? ?) -K0 /2 width=1/ /3 width=3/
 ]
 qed.
 
-lemma ltpss_ldrop_trans_be: ∀L1,L0,d1,e1. L1 [d1, e1] ▶* L0 →
+lemma ltpss_ldrop_trans_be: ∀L1,L0,d1,e1. L1 ▶* [d1, e1] L0 →
                             ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → d1 ≤ e2 → e2 ≤ d1 + e1 →
-                            ∃∃L. L [0, d1 + e1 - e2] ▶* L2 & ⇩[0, e2] L1 ≡ L.
-#L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0
-[ /2 width=3/
-| #L #L0 #_ #HL0 #IHL #L2 #e2 #HL02 #Hd1e2 #He2de1
-  elim (ltps_ldrop_trans_be … HL0 … HL02 Hd1e2 He2de1) -L0 #L0 #HL02 #HL0
-  elim (IHL … HL0 Hd1e2 He2de1) -L /3 width=3/
+                            ∃∃L. L ▶* [0, d1 + e1 - e2] L2 & ⇩[0, e2] L1 ≡ L.
+#L1 #L0 #d1 #e1 #H elim H -L1 -L0 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/
+| normalize #L #I #V #L2 #e2 #HL2 #_ #He2
+  lapply (le_n_O_to_eq … He2) -He2 #H destruct
+  lapply (ldrop_inv_refl … HL2) -HL2 #H destruct /2 width=3/
+| normalize #K1 #K0 #I #V1 #V0 #e1 #HK10 #HV10 #IHK10 #L2 #e2 #H #_ #He21
+  lapply (ldrop_inv_O1 … H) -H * * #He2 #HK0L2
+  [ -IHK10 -He21 destruct <minus_n_O /3 width=3/
+  | -HK10 -HV10 <minus_le_minus_minus_comm //
+    elim (IHK10 … HK0L2 ? ?) -K0 // /2 width=1/ /3 width=3/
+  ]
+| #K1 #K0 #I #V1 #V0 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHK10 #L2 #e2 #H #Hd1e2 #He2de1
+  elim (le_inv_plus_l … Hd1e2) #_ #He2
+  <minus_le_minus_minus_comm //
+  lapply (ldrop_inv_ldrop1 … H ?) -H // #HK0L2
+  elim (IHK10 … HK0L2 ? ?) -K0 /2 width=1/ /3 width=3/
 ]
 qed.
 
-lemma ltpss_ldrop_conf_le: ∀L0,L1,d1,e1. L0 [d1, e1] ▶* L1 →
+lemma ltpss_ldrop_conf_le: ∀L0,L1,d1,e1. L0 ▶* [d1, e1] L1 →
                            ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → e2 ≤ d1 →
-                           ∃∃L. L2 [d1 - e2, e1] ▶* L & ⇩[0, e2] L1 ≡ L.
-#L0 #L1 #d1 #e1 #H @(ltpss_ind … H) -L1
-[ /2 width=3/
-| #L #L1 #_ #HL1 #IHL #L2 #e2 #HL02 #He2d1
-  elim (IHL … HL02 He2d1) -L0 #L0 #HL20 #HL0
-  elim (ltps_ldrop_conf_le … HL1 … HL0 He2d1) -L /3 width=3/
+                           ∃∃L. L2 ▶* [d1 - e2, e1] L & ⇩[0, e2] L1 ≡ L.
+#L0 #L1 #d1 #e1 #H elim H -L0 -L1 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/
+| /2 width=3/
+| normalize #K0 #K1 #I #V0 #V1 #e1 #HK01 #HV01 #_ #L2 #e2 #H #He2
+  lapply (le_n_O_to_eq … He2) -He2 #He2 destruct
+  lapply (ldrop_inv_refl … H) -H #H destruct /3 width=3/
+| #K0 #K1 #I #V0 #V1 #d1 #e1 #HK01 #HV01 #IHK01 #L2 #e2 #H #He2d1
+  lapply (ldrop_inv_O1 … H) -H * * #He2 #HK0L2
+  [ -IHK01 -He2d1 destruct <minus_n_O /3 width=3/
+  | -HK01 -HV01 <minus_le_minus_minus_comm //
+    elim (IHK01 … HK0L2 ?) -K0 /2 width=1/ /3 width=3/
+  ]
 ]
 qed.
 
-lemma ltpss_ldrop_trans_le: ∀L1,L0,d1,e1. L1 [d1, e1] ▶* L0 →
+lemma ltpss_ldrop_trans_le: ∀L1,L0,d1,e1. L1 ▶* [d1, e1] L0 →
                             ∀L2,e2. ⇩[0, e2] L0 ≡ L2 → e2 ≤ d1 →
-                            ∃∃L. L [d1 - e2, e1] ▶* L2 & ⇩[0, e2] L1 ≡ L.
-#L1 #L0 #d1 #e1 #H @(ltpss_ind … H) -L0
-[ /2 width=3/
-| #L #L0 #_ #HL0 #IHL #L2 #e2 #HL02 #He2d1
-  elim (ltps_ldrop_trans_le … HL0 … HL02 He2d1) -L0 #L0 #HL02 #HL0
-  elim (IHL … HL0 He2d1) -L /3 width=3/
+                            ∃∃L. L ▶* [d1 - e2, e1] L2 & ⇩[0, e2] L1 ≡ L.
+#L1 #L0 #d1 #e1 #H elim H -L1 -L0 -d1 -e1
+[ #d1 #e1 #L2 #e2 #H >(ldrop_inv_atom1 … H) -H /2 width=3/
+| /2 width=3/
+| normalize #K1 #K0 #I #V1 #V0 #e1 #HK10 #HV10 #_ #L2 #e2 #H #He2
+  lapply (le_n_O_to_eq … He2) -He2 #He2 destruct
+  lapply (ldrop_inv_refl … H) -H #H destruct /3 width=3/
+| #K1 #K0 #I #V1 #V0 #d1 #e1 #HK10 #HV10 #IHK10 #L2 #e2 #H #He2d1
+  lapply (ldrop_inv_O1 … H) -H * * #He2 #HK0L2
+  [ -IHK10 -He2d1 destruct <minus_n_O /3 width=3/
+  | -HK10 -HV10 <minus_le_minus_minus_comm //
+    elim (IHK10 … HK0L2 ?) -K0 /2 width=1/ /3 width=3/
+  ]
 ]
 qed.