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 a47d224d3c0369107afada337c9fa547cc702c4d..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
@@ -12,46 +12,50 @@
 (*                                                                        *)
 (**************************************************************************)
 
+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".
-(*
-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.
+(* 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_trans: ∀L1,L,des1. ⇓[des1] L1 ≡ L → ∀L2,des2. ⇓[des2] L ≡ L2 →
-                    ⇓[des2 @ des1] L1 ≡ L2.
+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_lifts: ∀RR,RS,RP. 
+axiom aacr_aaa_csubc_lifts: ∀RR,RS,RP.
                               acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
-                              â\88\80L1,T,A. L1 â\8a¢ T ÷ A â\86\92 â\88\80L0,des. â\87\93[des] L0 ≡ L1 →
-                              â\88\80T0. â\87\91[des] T ≡ T0 → ∀L2. L2 [RP] ⊑ L0 →
+                              â\88\80L1,T,A. L1 â\8a¢ T ÷ A â\86\92 â\88\80L0,des. â\87©*[des] L0 ≡ L1 →
+                              â\88\80T0. â\87§*[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
+  @(s2 … HAtom … ◊) // /2 width=2/
+| * #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
+    @(cp2 … H1RP)
+  ]
+
+| #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/ *)
+  @(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)
@@ -63,11 +67,14 @@ axiom aacr_aaa_csubc_lifts: ∀RR,RS,RP.
     @(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
+| #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) →