syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / gcp_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/gcp_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/static/gcp_aaa.ma
deleted file mode 100644 (file)
index 31bcb5a..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/static/gcp_aaa.ma
+++ /dev/null
@@ -1,102 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/static/aaa_aaa.ma".
-include "basic_2/static/lsubc_drops.ma".
-
-(* GENERIC COMPUTATION PROPERTIES *******************************************)
-
-(* Main properties **********************************************************)
-
-(* Basic_1: was: sc3_arity_csubc *)
-theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
-                             gcp RR RS RP → gcr RR RS RP RP →
-                             ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀b,f,L0. ⬇*[b, f] L0 ≘ L1 →
-                             ∀T0. ⬆*[f] T ≘ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
-                             ⦃G, L2, T0⦄ ϵ[RP] 〚A〛.
-#RR #RS #RP #H1RP #H2RP #G #L1 #T @(fqup_wf_ind_eq (Ⓣ) … G L1 T) -G -L1 -T
-#Z #Y #X #IH #G #L1 * [ * | * [ #p ] * ]
-[ #s #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct -IH
-  lapply (aaa_inv_sort … HA) -HA #H destruct
-  >(lifts_inv_sort1 … H0) -H0
-  lapply (acr_gcr … H1RP H2RP (⓪)) #HAtom
-  lapply (s4 … HAtom G L2 (Ⓔ)) /2 width=1 by/
-| #i #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
-  elim (aaa_inv_lref_drops … HA) -HA #I #K1 #V1 #HLK1 #HKV1
-  elim (lifts_inv_lref1 … H0) -H0 #j #Hf #H destruct
-  lapply (acr_gcr … H1RP H2RP A) #HA
-  lapply (drops_trans … HL01 … HLK1 ??) -HL01 [3: |*: // ] #H
-  elim (drops_split_trans … H) -H [ |*: /2 width=6 by after_uni_dx/ ] #Y #HLK0 #HY
-  lapply (drops_tls_at … Hf … HY) -Hf -HY #HY
-  elim (drops_inv_skip2 … HY) -HY #Z #K0 #HK01 #HZ #H destruct
-  elim (liftsb_inv_pair_sn … HZ) -HZ #V0 #HV10 #H destruct
-  elim (lifts_total V0 (𝐔❴↑j❵)) #V #HV0
-  elim (lsubc_drops_trans_isuni … HL20 … HLK0) -HL20 -HLK0 // #Y #HLK2 #H
-  elim (lsubc_inv_bind2 … H) -H *
-  [ #K2 #HK20 #H destruct
-    lapply (drops_isuni_fwd_drop2 … HLK2) // #HLK2b
-    lapply (s5 … HA ? G ? ? (Ⓔ) … HV0 ?) -HA
-    /4 width=11 by acr_lifts, fqup_lref, drops_inv_gen/
-  | #K2 #V2 #W2 #B #HKV2 #HK2V0 #HKV0B #_ #H1 #H2 destruct -IH -HLK1
-    lapply (drops_isuni_fwd_drop2 … HLK2) // #HLK2b
-    lapply (aaa_lifts … HKV1 … HK01 … HV10) -HKV1 -HK01 -HV10 #HKV0A
-    lapply (aaa_mono … HKV0B … HKV0A) #H destruct -HKV0B -HKV0A
-    elim (lifts_total V2 (𝐔❴↑j❵)) #V3 #HV23
-    lapply (s5 … HA … G … (Ⓔ) … (ⓝW2.V2) (ⓝV.V3) ????)
-    [3: |*: /2 width=9 by drops_inv_gen, lifts_flat/ ] -HLK2
-    lapply (s7 … HA G L2 (Ⓔ)) -HA /3 width=7 by acr_lifts/
-  ]
-| #l #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct -IH
-  elim (aaa_inv_gref … HA)
-| #V #T #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
-  elim (aaa_inv_abbr … HA) -HA #B #HV #HT
-  elim (lifts_inv_bind1 … H0) -H0 #V0 #T0 #HV0 #HT0 #H destruct
-  lapply (acr_gcr … H1RP H2RP A) #HA
-  lapply (acr_gcr … H1RP H2RP B) #HB
-  lapply (s1 … HB) -HB #HB
-  lapply (s6 … HA G L2 (Ⓔ) (Ⓔ)) /5 width=10 by lsubc_bind, liftsv_nil, drops_skip, ext2_pair/
-| #W #T #HG #HL #HT #Z0 #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
-  elim (aaa_inv_abst … HA) -HA #B #A #HW #HT #H destruct
-  elim (lifts_inv_bind1 … H0) -H0 #W0 #T0 #HW0 #HT0 #H destruct
-  @(acr_abst  … H1RP H2RP) /2 width=10 by/
-  #b3 #f3 #L3 #V3 #W3 #T3 #HL32 #HW03 #HT03 #H1B #H2B
-  elim (drops_lsubc_trans … H1RP … HL32 … HL20) -L2 #L2 #HL32 #HL20
-  lapply (aaa_lifts … HW … (f3∘f) L2 … W3 ?) -HW
-  [4: |*: /2 width=8 by drops_trans, lifts_trans/ ] #HW3
-  @(IH … ((⫯f3)∘⫯f) … (L2. ⓛW3)) -IH
-  /4 width=12 by lsubc_beta, drops_trans, drops_skip, lifts_trans, ext2_pair/
-| #V #T #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
-  elim (aaa_inv_appl … HA) -HA #B #HV #HT
-  elim (lifts_inv_flat1 … H0) -H0 #V0 #T0 #HV0 #HT0 #H destruct
-  lapply (IH … HT … HL01 … HT0 … HL20) -HT -HT0
-  /3 width=10 by drops_refl, lifts_refl/
-| #W #T #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
-  elim (aaa_inv_cast … HA) -HA #HW #HT
-  elim (lifts_inv_flat1 … H0) -H0 #W0 #T0 #HW0 #HT0 #H destruct
-  lapply (acr_gcr … H1RP H2RP A) #HA
-  lapply (s7 … HA G L2 (Ⓔ)) /3 width=10 by/
-]
-qed.
-
-(* Basic_1: was: sc3_arity *)
-lemma acr_aaa: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
-               ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L, T⦄ ϵ[RP] 〚A〛.
-/3 width=9 by drops_refl, lifts_refl, acr_aaa_csubc_lifts/ qed.
-
-lemma gcr_aaa: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
-               ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → RP G L T.
-#RR #RS #RP #H1RP #H2RP #G #L #T #A #HT
-lapply (acr_gcr … H1RP H2RP A) #HA
-@(s1 … HA) /2 width=4 by acr_aaa/
-qed.