- lambda_delta: we updated some notation

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

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 b0d28be560d4e98ecdbbe9d5289f01c3a15298ed..3f41b0083c12f81d75dfc662d6aa63ed04998644 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/unfold/tpss_tpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/unfold/tpss_tpss.ma
@@ -17,38 +17,40 @@ include "basic_2/unfold/tpss_lift.ma".
 
 (* PARTIAL UNFOLD ON TERMS **************************************************)
 
-(* Advanced properties ******************************************************)
+(* Advanced inversion lemmas ************************************************)
 
-lemma tpss_tps: ∀L,T1,T2,d. L ⊢ T1 [d, 1] ▶* T2 → L ⊢ T1 [d, 1] ▶ T2.
+lemma tpss_inv_SO2: ∀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.
+qed-.
+
+(* Advanced properties ******************************************************)
 
-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.
+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.
+                      ∃∃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.
+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.
+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.
+                     ∃∃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
@@ -58,10 +60,11 @@ lemma tpss_split_up: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶* T2 →
 ]
 qed.
 
-lemma tpss_inv_lift1_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ▶* U2 →
+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 // [ >commutative_plus /2 width=1/ ] -Hddt -Hdtde #HU1
@@ -71,23 +74,23 @@ 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.
+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.
+                       ∃∃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. 
+                       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.
+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.