X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Funfold%2Ftpss_tpss.ma;h=981402a245ee27f3b1b242bb9f048e406af6f78c;hb=13a37618a5cebc5e0088a7da213f1de033d281db;hp=57e4fb199c5227f9201af5572981bd9cdbd01463;hpb=78f21d7d9014e5c7655f58239e4f1a128ea2c558;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_tpss.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_tpss.ma
index 57e4fb199..981402a24 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/tpss_tpss.ma
@@ -19,75 +19,75 @@ include "Basic_2/unfold/tpss_lift.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma tpss_tps: ∀L,T1,T2,d. L ⊢ T1 [d, 1] ≫* T2 → L ⊢ T1 [d, 1] ≫ T2.
-#L #T1 #T2 #d #H @(tpss_ind … H) -H T2 //
+lemma tpss_tps: ∀L,T1,T2,d. L ⊢ T1 [d, 1] ▶* T2 → L ⊢ T1 [d, 1] ▶ T2.
+#L #T1 #T2 #d #H @(tpss_ind … H) -T2 //
 #T #T2 #_ #HT2 #IHT1
 lapply (tps_trans_ge … IHT1 … HT2 ?) //
 qed.
 
-lemma tpss_strip_eq: ∀L,T0,T1,d1,e1. L ⊢ T0 [d1, e1] ≫* T1 →
-                     ∀T2,d2,e2. L ⊢ T0 [d2, e2] ≫ T2 →
-                     ∃∃T. L ⊢ T1 [d2, e2] ≫ T & L ⊢ T2 [d1, e1] ≫* T.
-/3/ qed.
+lemma tpss_strip_eq: ∀L,T0,T1,d1,e1. L ⊢ T0 [d1, e1] ▶* T1 →
+                     ∀T2,d2,e2. L ⊢ T0 [d2, e2] ▶ T2 →
+                     ∃∃T. L ⊢ T1 [d2, e2] ▶ T & L ⊢ T2 [d1, e1] ▶* T.
+/3 width=3/ qed.
 
-lemma tpss_strip_neq: ∀L1,T0,T1,d1,e1. L1 ⊢ T0 [d1, e1] ≫* T1 →
-                      ∀L2,T2,d2,e2. L2 ⊢ T0 [d2, e2] ≫ T2 →
+lemma tpss_strip_neq: ∀L1,T0,T1,d1,e1. L1 ⊢ T0 [d1, e1] ▶* T1 →
+                      ∀L2,T2,d2,e2. L2 ⊢ T0 [d2, e2] ▶ T2 →
                       (d1 + e1 ≤ d2 ∨ d2 + e2 ≤ d1) →
-                      ∃∃T. L2 ⊢ T1 [d2, e2] ≫ T & L1 ⊢ T2 [d1, e1] ≫* T.
-/3/ qed.
+                      ∃∃T. L2 ⊢ T1 [d2, e2] ▶ T & L1 ⊢ T2 [d1, e1] ▶* T.
+/3 width=3/ qed.
 
-lemma tpss_strap1_down: ∀L,T1,T0,d1,e1. L ⊢ T1 [d1, e1] ≫* T0 →
-                        ∀T2,d2,e2. L ⊢ T0 [d2, e2] ≫ T2 → d2 + e2 ≤ d1 →
-                        ∃∃T. L ⊢ T1 [d2, e2] ≫ T & L ⊢ T [d1, e1] ≫* T2.
-/3/ qed.
+lemma tpss_strap1_down: ∀L,T1,T0,d1,e1. L ⊢ T1 [d1, e1] ▶* T0 →
+                        ∀T2,d2,e2. L ⊢ T0 [d2, e2] ▶ T2 → d2 + e2 ≤ d1 →
+                        ∃∃T. L ⊢ T1 [d2, e2] ▶ T & L ⊢ T [d1, e1] ▶* T2.
+/3 width=3/ qed.
 
-lemma tpss_strap2_down: ∀L,T1,T0,d1,e1. L ⊢ T1 [d1, e1] ≫ T0 →
-                        ∀T2,d2,e2. L ⊢ T0 [d2, e2] ≫* T2 → d2 + e2 ≤ d1 →
-                        ∃∃T. L ⊢ T1 [d2, e2] ≫* T & L ⊢ T [d1, e1] ≫ T2.
-/3/ qed.
+lemma tpss_strap2_down: ∀L,T1,T0,d1,e1. L ⊢ T1 [d1, e1] ▶ T0 →
+                        ∀T2,d2,e2. L ⊢ T0 [d2, e2] ▶* T2 → d2 + e2 ≤ d1 →
+                        ∃∃T. L ⊢ T1 [d2, e2] ▶* T & L ⊢ T [d1, e1] ▶ T2.
+/3 width=3/ qed.
 
-lemma tpss_split_up: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫* T2 →
+lemma tpss_split_up: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶* T2 →
                      ∀i. d ≤ i → i ≤ d + e →
-                     ∃∃T. L ⊢ T1 [d, i - d] ≫* T & L ⊢ T [i, d + e - i] ≫* T2.
-#L #T1 #T2 #d #e #H #i #Hdi #Hide @(tpss_ind … H) -H T2
-[ /2/
+                     ∃∃T. L ⊢ T1 [d, i - d] ▶* T & L ⊢ T [i, d + e - i] ▶* T2.
+#L #T1 #T2 #d #e #H #i #Hdi #Hide @(tpss_ind … H) -T2
+[ /2 width=3/
 | #T #T2 #_ #HT12 * #T3 #HT13 #HT3
-  elim (tps_split_up … HT12 … Hdi Hide) -HT12 Hide #T0 #HT0 #HT02
-  elim (tpss_strap1_down … HT3 … HT0 ?) -T [2: <plus_minus_m_m_comm // ]
+  elim (tps_split_up … HT12 … Hdi Hide) -HT12 -Hide #T0 #HT0 #HT02
+  elim (tpss_strap1_down … HT3 … HT0 ?) -T [2: >commutative_plus /2 width=1/ ]
   /3 width=7 by ex2_1_intro, step/ (**) (* just /3 width=7/ is too slow *)
 ]
 qed.
 
-lemma tpss_inv_lift1_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫* U2 →
-                         ∀K,d,e. ↓[d, e] L ≡ K → ∀T1. ↑[d, e] T1 ≡ U1 →
+lemma tpss_inv_lift1_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 →
+                         ∀K,d,e. ⇩[d, e] L ≡ K → ∀T1. ⇧[d, e] T1 ≡ U1 →
                          d ≤ dt → dt ≤ d + e → d + e ≤ dt + et →
-                         ∃∃T2. K ⊢ T1 [d, dt + et - (d + e)] ≫* T2 & ↑[d, e] T2 ≡ U2.
+                         ∃∃T2. K ⊢ T1 [d, dt + et - (d + e)] ▶* T2 & ⇧[d, e] T2 ≡ U2.
 #L #U1 #U2 #dt #et #HU12 #K #d #e #HLK #T1 #HTU1 #Hddt #Hdtde #Hdedet
 elim (tpss_split_up … HU12 (d + e) ? ?) -HU12 // -Hdedet #U #HU1 #HU2
-lapply (tpss_weak … HU1 d e ? ?) -HU1 // <plus_minus_m_m_comm // -Hddt Hdtde #HU1
-lapply (tpss_inv_lift1_eq … HU1 … HTU1) -HU1 #HU1 destruct -U1;
-elim (tpss_inv_lift1_ge … HU2 … HLK … HTU1 ?) -HU2 HLK HTU1 // <minus_plus_m_m /2/
+lapply (tpss_weak … HU1 d e ? ?) -HU1 // [ >commutative_plus /2 width=1/ ] -Hddt -Hdtde #HU1
+lapply (tpss_inv_lift1_eq … HU1 … HTU1) -HU1 #HU1 destruct
+elim (tpss_inv_lift1_ge … HU2 … HLK … HTU1 ?) -HU2 -HLK -HTU1 // <minus_plus_m_m /2 width=3/
 qed.
 
 (* Main properties **********************************************************)
 
-theorem tpss_conf_eq: ∀L,T0,T1,d1,e1. L ⊢ T0 [d1, e1] ≫* T1 →
-                      ∀T2,d2,e2. L ⊢ T0 [d2, e2] ≫* T2 →
-                      ∃∃T. L ⊢ T1 [d2, e2] ≫* T & L ⊢ T2 [d1, e1] ≫* T.
-/3/ qed.
+theorem tpss_conf_eq: ∀L,T0,T1,d1,e1. L ⊢ T0 [d1, e1] ▶* T1 →
+                      ∀T2,d2,e2. L ⊢ T0 [d2, e2] ▶* T2 →
+                      ∃∃T. L ⊢ T1 [d2, e2] ▶* T & L ⊢ T2 [d1, e1] ▶* T.
+/3 width=3/ qed.
 
-theorem tpss_conf_neq: ∀L1,T0,T1,d1,e1. L1 ⊢ T0 [d1, e1] ≫* T1 →
-                       ∀L2,T2,d2,e2. L2 ⊢ T0 [d2, e2] ≫* T2 →
+theorem tpss_conf_neq: ∀L1,T0,T1,d1,e1. L1 ⊢ T0 [d1, e1] ▶* T1 →
+                       ∀L2,T2,d2,e2. L2 ⊢ T0 [d2, e2] ▶* T2 →
                        (d1 + e1 ≤ d2 ∨ d2 + e2 ≤ d1) →
-                       ∃∃T. L2 ⊢ T1 [d2, e2] ≫* T & L1 ⊢ T2 [d1, e1] ≫* T.
-/3/ qed.
+                       ∃∃T. L2 ⊢ T1 [d2, e2] ▶* T & L1 ⊢ T2 [d1, e1] ▶* T.
+/3 width=3/ qed.
 
 theorem tpss_trans_eq: ∀L,T1,T,T2,d,e.
-                       L ⊢ T1 [d, e] ≫* T → L ⊢ T [d, e] ≫* T2 →
-                       L ⊢ T1 [d, e] ≫* T2. 
-/2/ qed.
+                       L ⊢ T1 [d, e] ▶* T → L ⊢ T [d, e] ▶* T2 →
+                       L ⊢ T1 [d, e] ▶* T2. 
+/2 width=3/ qed.
 
-theorem tpss_trans_down: ∀L,T1,T0,d1,e1. L ⊢ T1 [d1, e1] ≫* T0 →
-                         ∀T2,d2,e2. L ⊢ T0 [d2, e2] ≫* T2 → d2 + e2 ≤ d1 →
-                         ∃∃T. L ⊢ T1 [d2, e2] ≫* T & L ⊢ T [d1, e1] ≫* T2.
-/3/ qed.
+theorem tpss_trans_down: ∀L,T1,T0,d1,e1. L ⊢ T1 [d1, e1] ▶* T0 →
+                         ∀T2,d2,e2. L ⊢ T0 [d2, e2] ▶* T2 → d2 + e2 ≤ d1 →
+                         ∃∃T. L ⊢ T1 [d2, e2] ▶* T & L ⊢ T [d1, e1] ▶* T2.
+/3 width=3/ qed.