X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc%2Fgcp%2Fgcp_cr.etc;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc%2Fgcp%2Fgcp_cr.etc;h=0000000000000000000000000000000000000000;hb=09b4420070d6a71990e16211e499b51dbb0742cb;hp=d8d3bbc83af59b8126afe72ba022a242c5b76648;hpb=bba53a83579540bc3925d47d679e2aad22e85755;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/gcp/gcp_cr.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/gcp/gcp_cr.etc deleted file mode 100644 index d8d3bbc83..000000000 --- a/matita/matita/contribs/lambdadelta/basic_2/etc/gcp/gcp_cr.etc +++ /dev/null @@ -1,177 +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/notation/relations/ineint_5.ma". -include "basic_2/grammar/aarity.ma". -include "basic_2/multiple/mr2_mr2.ma". -include "basic_2/multiple/lifts_lift_vector.ma". -include "basic_2/multiple/drops_drop.ma". -include "basic_2/computation/gcp.ma". - -(* GENERIC COMPUTATION PROPERTIES *******************************************) - -definition S0 ≝ λC:candidate. ∀G,L2,L1,T1,d,e. - C G L1 T1 → ∀T2. ⇩[Ⓕ, d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → C G L2 T2. - -definition S0s ≝ λC:candidate. - ∀G,L1,L2,des. ⇩*[Ⓕ, des] L2 ≡ L1 → - ∀T1,T2. ⇧*[des] T1 ≡ T2 → C G L1 T1 → C G L2 T2. - -(* Note: this is Girard's CR1 *) -definition S1 ≝ λRP,C:candidate. - ∀G,L,T. C G L T → RP G L T. - -(* Note: this is Tait's iii, or Girard's CR4 *) -definition S2 ≝ λRR:relation4 genv lenv term term. λRS:relation term. λRP,C:candidate. - ∀G,L,Vs. all … (RP G L) Vs → - ∀T. 𝐒⦃T⦄ → NF … (RR G L) RS T → C G L (ⒶVs.T). - -(* Note: this generalizes Tait's ii *) -definition S3 ≝ λC:candidate. - ∀a,G,L,Vs,V,T,W. - C G L (ⒶVs.ⓓ{a}ⓝW.V.T) → C G L (ⒶVs.ⓐV.ⓛ{a}W.T). - -definition S4 ≝ λRP,C:candidate. - ∀G,L,Vs. all … (RP G L) Vs → ∀k. C G L (ⒶVs.⋆k). - -definition S5 ≝ λC:candidate. ∀I,G,L,K,Vs,V1,V2,i. - ⇩[i] L ≡ K.ⓑ{I}V1 → ⇧[0, i+1] V1 ≡ V2 → - C G L (ⒶVs.V2) → C G L (ⒶVs.#i). - -definition S6 ≝ λRP,C:candidate. - ∀G,L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s → - ∀a,V,T. C G (L.ⓓV) (ⒶV2s.T) → RP G L V → C G L (ⒶV1s.ⓓ{a}V.T). - -definition S7 ≝ λC:candidate. - ∀G,L,Vs,T,W. C G L (ⒶVs.T) → C G L (ⒶVs.W) → C G L (ⒶVs.ⓝW.T). - -(* requirements for the generic reducibility candidate *) -record gcr (RR:relation4 genv lenv term term) (RS:relation term) (RP,C:candidate) : Prop ≝ -{ (* s0: S0 C; *) - s1: S1 RP C; - s2: S2 RR RS RP C; - s3: S3 C; - s4: S4 RP C; - s5: S5 C; - s6: S6 RP C; - s7: S7 C -}. - -(* the functional construction for candidates *) -definition cfun: candidate → candidate → candidate ≝ - λC1,C2,G,K,T. ∀V. C1 G K V → C2 G K (ⓐV.T). - -(* the reducibility candidate associated to an atomic arity *) -let rec acr (RP:candidate) (A:aarity) on A: candidate ≝ -match A with -[ AAtom ⇒ RP -| APair B A ⇒ cfun (acr RP B) (acr RP A) -]. - -interpretation - "candidate of reducibility of an atomic arity (abstract)" - 'InEInt RP G L T A = (acr RP A G L T). - -(* Basic properties *********************************************************) -(* -(* Basic_1: was: sc3_lift1 *) -lemma gcr_lifts: ∀C. S0 C → S0s C. -#C #HC #G #L1 #L2 #des #H elim H -L1 -L2 -des -[ #L #T1 #T2 #H #HT1 <(lifts_inv_nil … H) -H // -| #L1 #L #L2 #des #d #e #_ #HL2 #IHL #T2 #T1 #H #HLT2 - elim (lifts_inv_cons … H) -H /3 width=10 by/ -] -qed. -*) -axiom rp_lift: ∀RP. S0 RP. - - -axiom rp_lifts: ∀RR,RS,RP. gcr RR RS RP RP → - ∀des,G,L0,L,V,V0. ⇩*[Ⓕ, des] L0 ≡ L → ⇧*[des] V ≡ V0 → - RP G L V → RP G L0 V0. -(* -#RR #RS #RP #HRP #des #G #L0 #L #V #V0 #HL0 #HV0 #HV -@gcr_lifts /width=7 by/ -@(s0 … HRP) -qed. -*) -(* Basic_1: was only: sns3_lifts1 *) -axiom rp_liftsv_all: ∀RR,RS,RP. gcr RR RS RP RP → - ∀des,G,L0,L,Vs,V0s. ⇩*[Ⓕ, des] L0 ≡ L → ⇧*[des] Vs ≡ V0s → - all … (RP G L) Vs → all … (RP G L0) V0s. -(* -#RR #RS #RP #HRP #des #G #L0 #L #Vs #V0s #HL0 #H elim H -Vs -V0s normalize // -#T1s #T2s #T1 #T2 #HT12 #_ #IHT2s * /3 width=7 by rp_lifts, conj/ -qed. -*) - -lemma gcr_lift: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP → - ∀A. S0 (acr RP A). -#RR #RS #RP #H1RP #H2RP #A elim A -A /2 width=7 by rp_lift/ -#B #A #IHB #IHA #G #L2 #L1 #T1 #d #e #IH #T2 #HL21 #HT12 #V #HB -@(IHA … HL21) [3: @(lift_flat … HT12) |1: skip | - -(* Basic_1: was: - sc3_sn3 sc3_abst sc3_appl sc3_abbr sc3_bind sc3_cast sc3_lift -*) -lemma acr_gcr: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP → - ∀A. gcr RR RS RP (acr RP A). -#RR #RS #RP #H1RP #H2RP #A elim A -A // -#B #A #IHB #IHA @mk_gcr -[ #G #L #T #H - elim (cp1 … H1RP G L) #k #HK - lapply (H (⋆k) ?) -H - [ lapply (s2 … IHB G L (◊) … HK) // - | #H @(cp2 … H1RP … k) @(s1 … IHA) // - ] -| #G #L #Vs #HVs #T #H1T #H2T #V #HB - lapply (s1 … IHB … HB) #HV - @(s2 … IHA … (V @ Vs)) - /3 width=14 by rp_liftsv_all, gcp_lifts, cp0, lifts_simple_dx, conj/ -| #a #G #L #Vs #U #T #W #HA #V #HB - @(s3 … IHA … (V @ Vs)) /2 width=1 by/ -| #G #L #Vs #HVs #k #V #HB - lapply (s1 … IHB … HB) #HV - @(s4 … IHA … (V @ Vs)) /3 width=7 by rp_liftsv_all, conj/ -| #I #G #L #K #Vs #V1 #V2 #i #HLK #HV12 #HA #V #HB - @(s5 … IHA … (V @ Vs) … HLK HV12) /2 width=1 by/ -| #G #L #V1s #V2s #HV12s #a #W #T #HA #HW #V1 #HB - elim (lift_total V1 0 1) #V2 #HV12 - @(s6 … IHA … (V1 @ V1s) (V2 @ V2s)) /2 width=1 by liftv_cons/ - @HA @(gcr_lift … H1RP H2RP … HB … HV12) /2 width=2 by drop_drop/ -| #G #L #Vs #T #W #HA #HW #V #HB - @(s7 … IHA … (V @ Vs)) /2 width=1 by/ -] -qed. - -lemma acr_abst: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP → - ∀a,G,L,W,T,B,A. ⦃G, L, W⦄ ϵ[RP] 〚B〛 → ( - ∀V. ⦃G, L, V⦄ ϵ[RP] 〚B〛 → ⦃G, L.ⓓⓝW.V, T⦄ ϵ[RP] 〚A〛 - ) → - ⦃G, L, ⓛ{a}W.T⦄ ϵ[RP] 〚②B.A〛. -#RR #RS #RP #H1RP #H2RP #a #G #L #W #T #B #A #HW #HA #L0 #V0 #X #des #HL0 #H #HB -lapply (acr_gcr … H1RP H2RP A) #HCA -lapply (acr_gcr … H1RP H2RP B) #HCB -elim (lifts_inv_bind1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct -lapply (gcr_lifts … HL0 … HW0 HW) -HW [ @(s0 … HCB) ] #HW0 -lapply (s3 … HCA … a G L0 (◊)) #H @H -H -lapply (s6 … HCA G L0 (◊) (◊) ?) // #H @H -H -[ @(HA … HL0) // -| lapply (s1 … HCB) -HCB #HCB - lapply (s7 … H2RP G L0 (◊)) /3 width=1 by/ -] -qed. - -(* Basic_1: removed theorems 2: sc3_arity_gen sc3_repl *) -(* Basic_1: removed local theorems 1: sc3_sn3_abst *)