X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Facp_aaa.ma;h=3656d36f66f42ec22e293262756ae6d41c85faa2;hb=ab0d181f9a89f461a9c280f42a949a2dc2abe44c;hp=2ffff40df125eb499b27660dafbae2881ac784d0;hpb=fba384e357ed3c8781fc018c2c16f2b40df144af;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/acp_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/acp_aaa.ma
index 2ffff40df..3656d36f6 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/acp_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/acp_aaa.ma
@@ -12,28 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unfold/lifts_lifts.ma".
-include "basic_2/unfold/ldrops_ldrops.ma".
+include "basic_2/substitution/lifts_lifts.ma".
+include "basic_2/substitution/ldrops_ldrops.ma".
 include "basic_2/static/aaa_lifts.ma".
 include "basic_2/static/aaa_aaa.ma".
 include "basic_2/computation/lsubc_ldrops.ma".
 
 (* ABSTRACT COMPUTATION PROPERTIES ******************************************)
 
-(* Main propertis ***********************************************************)
+(* Main properties **********************************************************)
 
 (* Basic_1: was: sc3_arity_csubc *)
 theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
-                              acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
-                              ∀L1,T,A. L1 ⊢ T ⁝ A → ∀L0,des. ⇩*[des] L0 ≡ L1 →
-                              ∀T0. ⇧*[des] T ≡ T0 → ∀L2. L2 ⊑[RP] L0 →
-                              ⦃L2, T0⦄ ϵ[RP] 〚A〛.
-#RR #RS #RP #H1RP #H2RP #L1 #T #A #H elim H -L1 -T -A
-[ #L #k #L0 #des #HL0 #X #H #L2 #HL20
+                              acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
+                              ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀L0,des. ⇩*[des] L0 ≡ L1 →
+                              ∀T0. ⇧*[des] T ≡ T0 → ∀L2. G ⊢ L2 ⊑[RP] L0 →
+                              ⦃G, L2, T0⦄ ϵ[RP] 〚A〛.
+#RR #RS #RP #H1RP #H2RP #G #L1 #T #A #H elim H -G -L1 -T -A
+[ #G #L #k #L0 #des #HL0 #X #H #L2 #HL20
   >(lifts_inv_sort1 … H) -H
   lapply (aacr_acr … H1RP H2RP (⓪)) #HAtom
-  @(s2 … HAtom … ◊) // /2 width=2/
-| #I #L1 #K1 #V1 #B #i #HLK1 #HKV1B #IHB #L0 #des #HL01 #X #H #L2 #HL20
+  @(s4 … HAtom … (◊)) //
+| #I #G #L1 #K1 #V1 #B #i #HLK1 #HKV1B #IHB #L0 #des #HL01 #X #H #L2 #HL20
   lapply (aacr_acr … H1RP H2RP B) #HB
   elim (lifts_inv_lref1 … H) -H #i1 #Hi1 #H destruct
   lapply (ldrop_fwd_ldrop2 … HLK1) #HK1b
@@ -43,59 +43,50 @@ theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
   elim (lsubc_ldrop_O1_trans … HL20 … HL0) -HL0 #X #HLK2 #H
   elim (lsubc_inv_pair2 … H) -H *
   [ #K2 #HK20 #H destruct
-    generalize in match HLK2; generalize in match I; -HLK2 -I * #HLK2
-    [ elim (lift_total V0 0 (i0 +1)) #V #HV0
-      elim (lifts_lift_trans  … Hi0 … Hdes0 … HV10 … HV0) -HV10 #V2 #HV12 #HV2
-      @(s4 … HB … ◊ … HV0 HLK2) /3 width=7/ (* uses IHB HL20 V2 HV0 *)
-    | @(s2 … HB … ◊) // /2 width=3/
-    ]
+    elim (lift_total V0 0 (i0 +1)) #V #HV0
+    elim (lifts_lift_trans  … Hi0 … Hdes0 … HV10 … HV0) -HV10 #V2 #HV12 #HV2
+    @(s5 … HB … (◊) … HV0 HLK2) /3 width=7 by ldrops_cons, lifts_cons/ (* Note: uses IHB HL20 V2 HV0 *)
   | -HLK1 -IHB -HL01 -HL20 -HK1b -Hi0 -Hdes0
-    #K2 #V2 #A2 #HKV2A #HKV0A #_ #H1 #H2 destruct
+    #K2 #V2 #A2 #HKV2A #H1KV0A #H2KV0A #_ #H1 #H2 destruct
     lapply (ldrop_fwd_ldrop2 … HLK2) #HLK2b
     lapply (aaa_lifts … HK01 … HV10 HKV1B) -HKV1B -HK01 -HV10 #HKV0B
-    >(aaa_mono … HKV0A … HKV0B) in HKV2A; -HKV0A -HKV0B #HKV2B
+    lapply (aaa_mono … H2KV0A … HKV0B) #H destruct -H2KV0A -HKV0B
+    elim (lift_total V0 0 (i0 +1)) #V3 #HV03
     elim (lift_total V2 0 (i0 +1)) #V #HV2
-    @(s4 … HB … ◊ … HV2 HLK2)
-    @(s7 … HB … HKV2B) //
+    @(s5 … HB … (◊) … (ⓝV3.V) … HLK2) [2: /2 width=1 by lift_flat/ ]
+    @(s7 … HB … (◊)) [ @(s8 … HB … HKV2A) // | @(s8 … HB … H1KV0A) // ]
   ]
-| #a #L #V #T #B #A #_ #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL20
+| #a #G #L #V #T #B #A #_ #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL20
   elim (lifts_inv_bind1 … H) -H #V0 #T0 #HV0 #HT0 #H destruct
   lapply (aacr_acr … H1RP H2RP A) #HA
   lapply (aacr_acr … H1RP H2RP B) #HB
   lapply (s1 … HB) -HB #HB
-  @(s5 … HA … ◊ ◊) // /3 width=5/
-| #a #L #W #T #B #A #HLWB #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL02
+  @(s6 … HA … (◊) (◊)) /3 width=5 by lsubc_pair, ldrops_skip, liftv_nil/
+| #a #G #L #W #T #B #A #HLWB #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL02
   elim (lifts_inv_bind1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
-  @(aacr_abst  … H1RP H2RP)
-  [ lapply (aacr_acr … H1RP H2RP B) #HB
-    @(s1 … HB) /2 width=5/
-  | -IHB
-    #L3 #V3 #T3 #des3 #HL32 #HT03 #HB
-    elim (lifts_total des3 W0) #W2 #HW02
-    elim (ldrops_lsubc_trans … H1RP H2RP … HL32 … HL02) -L2 #L2 #HL32 #HL20
-    lapply (aaa_lifts … L2 W2 … (des @@ des3) … HLWB) -HLWB /2 width=3/ #HLW2B
-    @(IHA (L2. ⓛW2) … (des + 1 @@ des3 + 1)) -IHA
-    /2 width=3/ /3 width=5/
-  ]
-| #L #V #T #B #A #_ #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL20
+  @(aacr_abst  … H1RP H2RP) [ /2 width=5 by/ ]
+  #L3 #V3 #W3 #T3 #des3 #HL32 #HW03 #HT03 #H1B #H2B
+  elim (ldrops_lsubc_trans … H1RP H2RP … HL32 … HL02) -L2 #L2 #HL32 #HL20
+  lapply (aaa_lifts … L2 W3 … (des @@ des3) … HLWB) -HLWB /2 width=3 by ldrops_trans, lifts_trans/ #HLW2B
+  @(IHA (L2. ⓛW3) … (des + 1 @@ des3 + 1)) -IHA /2 width=3/ /3 width=5 by lsubc_abbr, ldrops_trans, ldrops_skip/
+| #G #L #V #T #B #A #_ #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL20
   elim (lifts_inv_flat1 … H) -H #V0 #T0 #HV0 #HT0 #H destruct
-  /3 width=10/
-| #L #V #T #A #_ #_ #IH1A #IH2A #L0 #des #HL0 #X #H #L2 #HL20
+  /3 width=10 by ldrops_nil, lifts_nil/
+| #G #L #V #T #A #_ #_ #IH1A #IH2A #L0 #des #HL0 #X #H #L2 #HL20
   elim (lifts_inv_flat1 … H) -H #V0 #T0 #HV0 #HT0 #H destruct
   lapply (aacr_acr … H1RP H2RP A) #HA
-  lapply (s1 … HA) #H
-  @(s6 … HA … ◊) /2 width=5/ /3 width=5/
+  @(s7 … HA … (◊)) /2 width=5 by/
 ]
 qed.
 
 (* Basic_1: was: sc3_arity *)
-lemma aacr_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
-                ∀L,T,A. L ⊢ T ⁝ A → ⦃L, T⦄ ϵ[RP] 〚A〛.
-/2 width=8/ qed.
+lemma aacr_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
+                ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L, T⦄ ϵ[RP] 〚A〛.
+/2 width=8 by ldrops_nil, lifts_nil, aacr_aaa_csubc_lifts/ qed.
 
-lemma acp_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
-               ∀L,T,A. L ⊢ T ⁝ A → RP L T.
-#RR #RS #RP #H1RP #H2RP #L #T #A #HT
+lemma acp_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
+               ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → RP G L T.
+#RR #RS #RP #H1RP #H2RP #G #L #T #A #HT
 lapply (aacr_acr … H1RP H2RP A) #HA
-@(s1 … HA) /2 width=4/
+@(s1 … HA) /2 width=4 by aacr_aaa/
 qed.