eliminators of arited terms based on "big tree" proper computation

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / aaa_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma
index bcbb5c20785f91730ac540b4ccac6fcc713c2f9a..ea039002f6202dd34dc936519da205c2d14fd01a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/aaa_lift.ma
@@ -17,7 +17,7 @@ include "basic_2/static/aaa.ma".
 
 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
 
-(* Properties concerning basic relocation ***********************************)
+(* Properties on basic relocation *******************************************)
 
 lemma aaa_lift: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀L2,d,e. ⇩[d, e] L2 ≡ L1 →
                 ∀T2. ⇧[d, e] T1 ≡ T2 → ⦃G, L2⦄ ⊢ T2 ⁝ A.
@@ -26,23 +26,23 @@ lemma aaa_lift: ∀G,L1,T1,A. ⦃G, L1⦄ ⊢ T1 ⁝ A → ∀L2,d,e. ⇩[d, e]
   >(lift_inv_sort1 … H) -H //
 | #I #G #L1 #K1 #V1 #B #i #HLK1 #_ #IHB #L2 #d #e #HL21 #T2 #H
   elim (lift_inv_lref1 … H) -H * #Hid #H destruct
-  [ elim (ldrop_trans_le … HL21 … HLK1) -L1 /2 width=2/ #X #HLK2 #H
-    elim (ldrop_inv_skip2 … H) -H /2 width=1/ -Hid #K2 #V2 #HK21 #HV12 #H destruct
+  [ elim (ldrop_trans_le … HL21 … HLK1) -L1 /2 width=2 by lt_to_le/ #X #HLK2 #H
+    elim (ldrop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ -Hid #K2 #V2 #HK21 #HV12 #H destruct
     /3 width=8/
-  | lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1 // -Hid /3 width=8/
+  | lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1 /3 width=8 by aaa_lref/
   ]
 | #a #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
   elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  /4 width=4/
+  /4 width=4 by aaa_abbr, ldrop_skip/
 | #a #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
   elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  /4 width=4/
+  /4 width=4 by aaa_abst, ldrop_skip/
 | #G #L1 #V1 #T1 #B #A #_ #_ #IHB #IHA #L2 #d #e #HL21 #X #H
   elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  /3 width=4/
+  /3 width=4 by aaa_appl/
 | #G #L1 #V1 #T1 #A #_ #_ #IH1 #IH2 #L2 #d #e #HL21 #X #H
   elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct
-  /3 width=4/
+  /3 width=4 by aaa_cast/
 ]
 qed.
 
@@ -53,20 +53,20 @@ lemma aaa_inv_lift: ∀G,L2,T2,A. ⦃G, L2⦄ ⊢ T2 ⁝ A → ∀L1,d,e. ⇩[d,
   >(lift_inv_sort2 … H) -H //
 | #I #G #L2 #K2 #V2 #B #i #HLK2 #_ #IHB #L1 #d #e #HL21 #T1 #H
   elim (lift_inv_lref2 … H) -H * #Hid #H destruct
-  [ elim (ldrop_conf_lt … HL21 … HLK2) -L2 // -Hid /3 width=8/
-  | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 // -Hid /3 width=8/
+  [ elim (ldrop_conf_lt … HL21 … HLK2) -L2 /3 width=8 by aaa_lref/
+  | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 /3 width=8 by aaa_lref/
   ]
 | #a #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
   elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  /4 width=4/
+  /4 width=4 by aaa_abbr, ldrop_skip/
 | #a #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
   elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  /4 width=4/
+  /4 width=4 by aaa_abst, ldrop_skip/
 | #G #L2 #V2 #T2 #B #A #_ #_ #IHB #IHA #L1 #d #e #HL21 #X #H
   elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  /3 width=4/
+  /3 width=4 by aaa_appl/
 | #G #L2 #V2 #T2 #A #_ #_ #IH1 #IH2 #L1 #d #e #HL21 #X #H
   elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
-  /3 width=4/
+  /3 width=4 by aaa_cast/
 ]
 qed-.