- new extendedd beta-reductum involving native type annotation

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lsubc_ldrop.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_ldrop.ma
index a7c7c7a99be5922b2decdaf5d116f9f0eb6c7072..60b58598b8f57513f17543005d7932d05dd71871 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_ldrop.ma
@@ -24,16 +24,15 @@ include "basic_2/computation/lsubc.ma".
 lemma lsubc_ldrop_O1_trans: ∀RP,L1,L2. L1 ⊑[RP] L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
                             ∃∃K1. ⇩[0, e] L1 ≡ K1 & K1 ⊑[RP] K2.
 #RP #L1 #L2 #H elim H -L1 -L2
-[ #X #e #H
-  >(ldrop_inv_atom1 … H) -H /2 width=3/
+[ #X #e #H elim (ldrop_inv_atom1 … H) -H /2 width=3/
 | #I #L1 #L2 #V #_ #IHL12 #X #e #H
-  elim (ldrop_inv_O1 … H) -H * #He #H destruct
-  [ elim (IHL12 L2 0 ?) -IHL12 // #X #H <(ldrop_inv_refl … H) -H /3 width=3/
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #H destruct
+  [ elim (IHL12 L2 0) -IHL12 // #X #H <(ldrop_inv_O2 … H) -H /3 width=3/
   | elim (IHL12 … H) -L2 /3 width=3/
   ]
-| #L1 #L2 #V #W #A #HV #HW #_ #IHL12 #X #e #H
-  elim (ldrop_inv_O1 … H) -H * #He #H destruct
-  [ elim (IHL12 L2 0 ?) -IHL12 // #X #H <(ldrop_inv_refl … H) -H /3 width=7/
+| #L1 #L2 #V #W #A #HV #H1W #H2W #_ #IHL12 #X #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #H destruct
+  [ elim (IHL12 L2 0) -IHL12 // #X #H <(ldrop_inv_O2 … H) -H /3 width=8/
   | elim (IHL12 … H) -L2 /3 width=3/
   ]
 qed-.
@@ -44,12 +43,11 @@ lemma ldrop_lsubc_trans: ∀RR,RS,RP.
                          ∀L1,K1,d,e. ⇩[d, e] L1 ≡ K1 → ∀K2. K1 ⊑[RP] K2 →
                          ∃∃L2. L1 ⊑[RP] L2 & ⇩[d, e] L2 ≡ K2.
 #RR #RS #RP #Hacp #Hacr #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
-[ #d #e #X #H
-  >(lsubc_inv_atom1 … H) -H /2 width=3/
+[ #d #X #H elim (lsubc_inv_atom1 … H) -H /2 width=3/
 | #L1 #I #V1 #X #H
   elim (lsubc_inv_pair1 … H) -H *
   [ #K1 #HLK1 #H destruct /3 width=3/
-  | #K1 #W1 #A #HV1 #HW1 #HLK1 #H1 #H2 destruct /3 width=3/
+  | #K1 #V #W1 #A #HV1 #H1W1 #H2W1 #HLK1 #H1 #H2 #H3 destruct /3 width=4/
   ]
 | #L1 #K1 #I #V1 #e #_ #IHLK1 #K2 #HK12
   elim (IHLK1 … HK12) -K1 /3 width=5/
@@ -57,11 +55,12 @@ lemma ldrop_lsubc_trans: ∀RR,RS,RP.
   elim (lsubc_inv_pair1 … H) -H *
   [ #K2 #HK12 #H destruct
     elim (IHLK1 … HK12) -K1 /3 width=5/
-  | #K2 #W2 #A #HV2 #HW2 #HK12 #H1 #H2 destruct
+  | #K2 #V #W2 #A #HV2 #H1W2 #H2W2 #HK12 #H1 #H2 #H3 destruct
+    elim (lift_inv_flat1 … HV21) -HV21 #W3 #V3 #HW23 #HV3 #H destruct
     elim (IHLK1 … HK12) #K #HL1K #HK2
     lapply (aacr_acr … Hacp Hacr A) -Hacp -Hacr #HA
-    lapply (s7 … HA … HV2 … HLK1 HV21) -HV2
-    elim (lift_total W2 d e) /4 width=9/
+    lapply (s8 … HA … HV2 … HLK1 HV3) -HV2
+    lapply (s8 … HA … H1W2 … HLK1 HW23) -H1W2 /4 width=10/
   ]
 ]
 qed-.