More work on inserting UnsafeCoerce in argument applications only when needed.

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / static / aaa_ltpss.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss.ma b/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss.ma
index ed624a9df6472a8499249f4523969486a658dd81..c672f02fa6ffae2ee7f364b9f448e31d1dc4694d 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss.ma
@@ -21,8 +21,8 @@ include "basic_2/static/aaa_lift.ma".
 (* Properties about parallel unfold *****************************************)
 
 (* Note: lemma 500 *)
-lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 [d, e] ▶* L2 →
-                           ∀T2. L2 ⊢ T1 [d, e] ▶* T2 → L2 ⊢ T2 ⁝ A.
+lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 ▶* [d, e] L2 →
+                           ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → L2 ⊢ T2 ⁝ A.
 #L1 #T1 #A #H elim H -L1 -T1 -A
 [ #L1 #k #L2 #d #e #_ #T2 #H
   >(tpss_inv_sort1 … H) -H //
@@ -32,13 +32,14 @@ lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 [d, e]
     elim (lt_or_ge i d) #Hdi
     [ elim (ltpss_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
       elim (ltpss_inv_tpss11 … H ?) -H /2 width=1/ -Hdi #K2 #V2 #HK12 #HV12 #H destruct
-      /3 width=8/
+      /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
     | elim (lt_or_ge i (d + e)) #Hide
       [ elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
         elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K2 #V2 #HK12 #HV12 #H destruct
-        /3 width=8/
+        /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
       | -Hdi
-        lapply (ltpss_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide /3 width=8/
+        lapply (ltpss_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide
+        /3 width=8 by aaa_lref/ (**) (* too slow without trace *)
       ]
     ]
   | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #HVW2 #HWT2
@@ -48,9 +49,9 @@ lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 [d, e]
     lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 #HLK2
     lapply (tpss_trans_eq … HV12 HVW2) -V2 /3 width=7/
   ]
-| #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
+| #a #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
   elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=4/
-| #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
+| #a #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
   elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=4/
 | #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
   elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=4/
@@ -59,18 +60,18 @@ lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 [d, e]
 ]
 qed.
 
-lemma aaa_ltpss_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 [d, e] ▶* L2 →
-                          ∀T2. L2 ⊢ T1 [d, e] ▶ T2 → L2 ⊢ T2 ⁝ A.
+lemma aaa_ltpss_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 ▶* [d, e] L2 →
+                          ∀T2. L2 ⊢ T1 ▶ [d, e] T2 → L2 ⊢ T2 ⁝ A.
 /3 width=7/ qed.
 
 lemma aaa_ltpss_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
-                      ∀L2,d,e. L1 [d, e] ▶* L2 → L2 ⊢ T ⁝ A.
+                      ∀L2,d,e. L1 ▶* [d, e] L2 → L2 ⊢ T ⁝ A.
 /2 width=7/ qed.
 
 lemma aaa_tpss_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
-                     ∀T2,d,e. L ⊢ T1 [d, e] ▶* T2 → L ⊢ T2 ⁝ A.
+                     ∀T2,d,e. L ⊢ T1 ▶* [d, e] T2 → L ⊢ T2 ⁝ A.
 /2 width=7/ qed.
 
 lemma aaa_tps_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
-                    ∀T2,d,e. L ⊢ T1 [d, e] ▶ T2 → L ⊢ T2 ⁝ A.
+                    ∀T2,d,e. L ⊢ T1 ▶ [d, e] T2 → L ⊢ T2 ⁝ A.
 /2 width=7/ qed.