- support for atomic arities and candidates of reducibility started

[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 a8492845333c75d7db27c49e501e832f53d1ee8b..cd7e666b27a65880cb0c697c6895062143c808ec 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
@@ -12,15 +12,15 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic-2/substitution/tps_tps.ma".
-include "Basic-2/unfold/tpss_lift.ma".
+include "Basic_2/substitution/tps_tps.ma".
+include "Basic_2/unfold/tpss_lift.ma".
 
 (* PARTIAL UNFOLD ON TERMS **************************************************)
 
 (* 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 //
+#L #T1 #T2 #d #H @(tpss_ind … H) -T2 //
 #T #T2 #_ #HT2 #IHT1
 lapply (tps_trans_ge … IHT1 … HT2 ?) //
 qed.
@@ -28,32 +28,32 @@ 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.
+/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 →
                       (d1 + e1 ≤ d2 ∨ d2 + e2 ≤ d1) →
                       ∃∃T. L2 ⊢ T1 [d2, e2] ≫ T & L1 ⊢ T2 [d1, e1] ≫* T.
-/3/ qed.
+/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.
+/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.
+/3 width=3/ qed.
 
 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/
+#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.
@@ -64,9 +64,9 @@ lemma tpss_inv_lift1_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫* 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 **********************************************************)
@@ -74,20 +74,20 @@ 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/ qed.
+/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 →
                        (d1 + e1 ≤ d2 ∨ d2 + e2 ≤ d1) →
                        ∃∃T. L2 ⊢ T1 [d2, e2] ≫* T & L1 ⊢ T2 [d1, e1] ≫* T.
-/3/ qed.
+/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.
+/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.
+/3 width=3/ qed.