the support for candidates of reducibility continues ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / computation / acp_aaa.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/acp_aaa.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/acp_aaa.ma
index 537d5b235d9a0869c5cdf0dfa363bfef344564e4..002fe017154fd7733007ba31fb4e875f36348cdb 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/computation/acp_aaa.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/computation/acp_aaa.ma
@@ -12,45 +12,74 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "Basic_2/unfold/lifts_lifts.ma".
+include "Basic_2/unfold/ldrops_ldrops.ma".
 include "Basic_2/static/aaa.ma".
 include "Basic_2/computation/lsubc.ma".
 
+(* NOTE: The constant (0) can not be generalized *)
+axiom lsubc_ldrop_trans: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
+                         ∃∃K1. ⇩[0, e] L1 ≡ K1 & K1 [RP] ⊑ K2.
+
+axiom ldrops_lsubc_trans: ∀RP,L1,K1,des. ⇩*[des] L1 ≡ K1 → ∀K2. K1 [RP] ⊑ K2 →
+                          ∃∃L2. L1 [RP] ⊑ L2 & ⇩*[des] L2 ≡ K2.
+
 (* ABSTRACT COMPUTATION PROPERTIES ******************************************)
 
 (* Main propertis ***********************************************************)
 
-axiom aacr_aaa_csubc: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
-                        ∀L1,T,A. L1 ⊢ T ÷ A →
-                        ∀L2. L2 [RP] ⊑ L1 → {L2, T} [RP] ϵ 〚A〛.
+axiom 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⦄ [RP] ϵ 〚A〛.
 (*
 #RR #RS #RP #H1RP #H2RP #L1 #T #A #H elim H -L1 -T -A
-[ #L #k #L2 #HL2
+[ #L #k #L0 #des #HL0 #X #H #L2 #HL20
+  >(lifts_inv_sort1 … H) -H
   lapply (aacr_acr … H1RP H2RP 𝕒) #HAtom
   @(s2 … HAtom … ◊) // /2 width=2/
-| * #L #K #V #B #i #HLK #_ #IHB #L2 #HL2
+| * #L #K #V #B #i #HLK #_ #IHB #L0 #des #HL0 #X #H #L2 #HL20
+  elim (lifts_inv_lref1 … H) -H #i0 #Hi0 #H destruct
+  elim (ldrops_ldrop_trans … HL0 … HLK) -L #L #des1 #i1 #HL0 #HLK #Hi1 #Hdes1 
+
+  elim (lsubc_ldrop_trans … HL20 … HL0) -L0 #L0 #HL20 #HL0 
   [
   | lapply (aacr_acr … H1RP H2RP B) #HB
     @(s2 … HB … ◊) //
     @(cp2 … H1RP)
-| #L #V #T #B #A #_ #_ #IHB #IHA #L2 #HL2
+  ]
+
+| #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=1/
-| #L #W #T #B #A #_ #_ #IHB #IHA #L2 #HL2
-  lapply (aacr_acr … H1RP H2RP B) #HB
-  lapply (s1 … HB) -HB #HB
-  @(aacr_abst  … H1RP H2RP) /3 width=1/ -HB /4 width=3/
-| /3 width=1/
-| #L #V #T #A #_ #_ #IH1A #IH2A #L2 #HL2
+  @(s5 … HA … ◊ ◊) // /3 width=5/
+| #L #W #T #B #A #_ #_ #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/
+  | #L3 #V3 #T3 #des3 #HL32 #HT03 #HB
+    elim (lifts_total des3 W0) #W2 #HW02
+    elim (ldrops_lsubc_trans … HL32 … HL02) -L2 #L2 #HL32 #HL20
+    @(IHA (L2. 𝕓{Abst} W2) … (ss des @ ss des3))
+    /2 width=3/ /3 width=5/ /4 width=6/
+  ]
+| #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
+  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=1/ /3 width=1/
+  @(s6 … HA … ◊) /2 width=5/ /3 width=5/
 ]
 *)
 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
 lapply (aacr_acr … H1RP H2RP A) #HA
-@(s1 … HA) /2 width=4/
+@(s1 … HA) /2 width=8/
 qed.