the support for reducibility candidates evolves ,,,,

[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 f3863f38b81131dd91acb51d008ca0b1dd8cd3a7..a47d224d3c0369107afada337c9fa547cc702c4d 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
@@ -14,33 +14,55 @@
 
 include "Basic_2/static/aaa.ma".
 include "Basic_2/computation/lsubc.ma".
+(*
+axiom lsubc_ldrops_trans: ∀RP,L1,L2. L1 [RP] ⊑ L2 → ∀K2,des. ⇓[des] L2 ≡ K2 →
+                          ∃∃K1. ⇓[des] 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.
+
+axiom lifts_trans: ∀T1,T,des1. ⇑[des1] T1 ≡ T → ∀T2:term. ∀des2. ⇑[des2] T ≡ T2 →
+                   ⇑[des1 @ des2] T1 ≡ T2.
+
+axiom ldrops_trans: ∀L1,L,des1. ⇓[des1] L1 ≡ L → ∀L2,des2. ⇓[des2] L ≡ L2 →
+                    ⇓[des2 @ des1] L1 ≡ L2.
 
 (* 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 #L2 #HL2
   lapply (aacr_acr … H1RP H2RP 𝕒) #HAtom
-  @(s2 … HAtom … ◊) // /2 width=2/
-| * #L #K #V #B #i #HLK #_ #IHB #L2 #HL2
+  @(s2 … HAtom … ◊) // /2 width=2/ *)
+| (* * #L #K #V #B #i #HLK #_ #IHB #L2 #HL2
   [
   | lapply (aacr_acr … H1RP H2RP B) #HB
     @(s2 … HB … ◊) //
-    @(cp2 … H1RP)
-| #L #V #T #B #A #_ #_ #IHB #IHA #L2 #HL2
+(*    @(cp2 … H1RP) *)
+  ] *)
+| (* #L #V #T #B #A #_ #_ #IHB #IHA #L2 #HL2
   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/
+  @(s5 … HA … ◊ ◊) // /3 width=1/ *)
+| #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/
+  ]
 | /3 width=1/
 | #L #V #T #A #_ #_ #IH1A #IH2A #L2 #HL2
   lapply (aacr_acr … H1RP H2RP A) #HA
@@ -52,5 +74,5 @@ 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.