commit completed: now we support two versions of slicing for local

[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 2c352dc897065b59af89473183c304d18f5c001e..c2cd35475a0b4562f6bde13ce33bcdaf1952f735 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsubc_ldrop.ma
@@ -21,46 +21,52 @@ include "basic_2/computation/lsubc.ma".
 
 (* Basic_1: was: csubc_drop_conf_O *)
 (* Note: the constant 0 can not be generalized *)
-lemma lsubc_ldrop_O1_trans: ∀RP,G,L1,L2. G ⊢ L1 ⊑[RP] L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
-                            ∃∃K1. ⇩[0, e] L1 ≡ K1 & G ⊢ K1 ⊑[RP] K2.
+lemma lsubc_ldrop_O1_trans: ∀RP,G,L1,L2. G ⊢ L1 ⊑[RP] L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
+                            ∃∃K1. ⇩[s, 0, e] L1 ≡ K1 & G ⊢ K1 ⊑[RP] K2.
 #RP #G #L1 #L2 #H elim H -L1 -L2
-[ #X #e #H elim (ldrop_inv_atom1 … H) -H /2 width=3/
-| #I #L1 #L2 #V #_ #IHL12 #X #e #H
+[ #X #s #e #H elim (ldrop_inv_atom1 … H) -H /4 width=3 by ldrop_atom, ex2_intro/
+| #I #L1 #L2 #V #_ #IHL12 #X #s #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=3/
-  | elim (IHL12 … H) -L2 /3 width=3/
+  [ elim (IHL12 L2 s 0) -IHL12 // #X #H <(ldrop_inv_O2 … H) -H
+    /3 width=3 by lsubc_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … H) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
-| #L1 #L2 #V #W #A #HV #H1W #H2W #_ #IHL12 #X #e #H
+| #L1 #L2 #V #W #A #HV #H1W #H2W #_ #IHL12 #X #s #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/
+  [ elim (IHL12 L2 s 0) -IHL12 // #X #H <(ldrop_inv_O2 … H) -H
+    /3 width=8 by lsubc_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … H) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
   ]
+]
 qed-.
 
 (* Basic_1: was: csubc_drop_conf_rev *)
 lemma ldrop_lsubc_trans: ∀RR,RS,RP.
                          acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
-                         ∀G,L1,K1,d,e. ⇩[d, e] L1 ≡ K1 → ∀K2. G ⊢ K1 ⊑[RP] K2 →
-                         ∃∃L2. G ⊢ L1 ⊑[RP] L2 & ⇩[d, e] L2 ≡ K2.
+                         ∀G,L1,K1,d,e. ⇩[Ⓕ, d, e] L1 ≡ K1 → ∀K2. G ⊢ K1 ⊑[RP] K2 →
+                         ∃∃L2. G ⊢ L1 ⊑[RP] L2 & ⇩[Ⓕ, d, e] L2 ≡ K2.
 #RR #RS #RP #Hacp #Hacr #G #L1 #K1 #d #e #H elim H -L1 -K1 -d -e
-[ #d #X #H elim (lsubc_inv_atom1 … H) -H /2 width=3/
+[ #d #e #He #X #H elim (lsubc_inv_atom1 … H) -H
+  >He /2 width=3 by ex2_intro/
 | #L1 #I #V1 #X #H
   elim (lsubc_inv_pair1 … H) -H *
-  [ #K1 #HLK1 #H destruct /3 width=3/
-  | #K1 #V #W1 #A #HV1 #H1W1 #H2W1 #HLK1 #H1 #H2 #H3 destruct /3 width=4/
+  [ #K1 #HLK1 #H destruct /3 width=3 by lsubc_pair, ldrop_pair, ex2_intro/
+  | #K1 #V #W1 #A #HV1 #H1W1 #H2W1 #HLK1 #H1 #H2 #H3 destruct
+    /3 width=4 by lsubc_abbr, ldrop_pair, ex2_intro/
   ]
-| #L1 #K1 #I #V1 #e #_ #IHLK1 #K2 #HK12
-  elim (IHLK1 … HK12) -K1 /3 width=5/
-| #L1 #K1 #I #V1 #V2 #d #e #HLK1 #HV21 #IHLK1 #X #H
+| #I #L1 #K1 #V1 #e #_ #IHLK1 #K2 #HK12
+  elim (IHLK1 … HK12) -K1 /3 width=5 by lsubc_pair, ldrop_drop, ex2_intro/
+| #I #L1 #K1 #V1 #V2 #d #e #HLK1 #HV21 #IHLK1 #X #H
   elim (lsubc_inv_pair1 … H) -H *
   [ #K2 #HK12 #H destruct
-    elim (IHLK1 … HK12) -K1 /3 width=5/
+    elim (IHLK1 … HK12) -K1 /3 width=5 by lsubc_pair, ldrop_skip, ex2_intro/
   | #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 (s8 … HA … HV2 … HLK1 HV3) -HV2
-    lapply (s8 … HA … H1W2 … HLK1 HW23) -H1W2 /4 width=10/
+    lapply (s8 … HA … H1W2 … HLK1 HW23) -H1W2
+    /4 width=11 by lsubc_abbr, aaa_lift, ldrop_skip, ex2_intro/
   ]
 ]
 qed-.