- first properties of strongly normalizing terms

[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..1cab5d4b8f2b2a04c143d648dc3e190375732165 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
@@ -12,42 +12,87 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/static/aaa.ma".
-include "Basic_2/computation/lsubc.ma".
+include "Basic_2/unfold/lifts_lifts.ma".
+include "Basic_2/unfold/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 ***********************************************************)
 
-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〛.
-(*
+(* 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⦄ [RP] ϵ 〚A〛.
 #RR #RS #RP #H1RP #H2RP #L1 #T #A #H elim H -L1 -T -A
-[ #L #k #L2 #HL2
-  lapply (aacr_acr … H1RP H2RP 𝕒) #HAtom
+[ #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/
-| * #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
-  lapply (aacr_acr … H1RP H2RP A) #HA
+| #I #L1 #K1 #V1 #B #i #HLK1 #HKV1B #IHB #L0 #des #HL01 #X #H #L2 #HL20
   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
+  elim (lifts_inv_lref1 … H) -H #i1 #Hi1 #H destruct
+  lapply (ldrop_fwd_ldrop2 … HLK1) #HK1b
+  elim (ldrops_ldrop_trans … HL01 … HLK1) #X #des1 #i0 #HL0 #H #Hi0 #Hdes1
+  >(at_mono … Hi1 … Hi0) -i1
+  elim (ldrops_inv_skip2 … Hdes1 … H) -des1 #K0 #V0 #des0 #Hdes0 #HK01 #HV10 #H destruct
+  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/
+    ]
+  | -HLK1 -IHB -HL01 -HL20 -HK1b -Hi0 -Hdes0
+    #K2 #V2 #A2 #HKV2A #HKV0A #_ #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
+    elim (lift_total V2 0 (i0 +1)) #V #HV2
+    @(s4 … HB … ◊ … HV2 HLK2)
+    @(s7 … HB … HKV2B) //
+  ]
+| #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
-  @(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 #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
+  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/
 ]
-*)
+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⦄ [RP] ϵ 〚A〛.
+/2 width=8/ 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