X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Fcomputation%2Facp_cr.ma;h=6eb71054b54a2ffc560c20f1cf6548245ab5a4ef;hb=f21509c476b20e5446335c967b1e81f87ceb4f6c;hp=9908cfd16cc4c84ac6f62d1c913770c111f8154b;hpb=d833e40ce45e301a01ddd9ea66c29fb2b34bb685;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/computation/acp_cr.ma b/matita/matita/contribs/lambda_delta/Basic_2/computation/acp_cr.ma
index 9908cfd16..6eb71054b 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/computation/acp_cr.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/computation/acp_cr.ma
@@ -13,7 +13,9 @@
 (**************************************************************************)
 
 include "Basic_2/grammar/aarity.ma".
+include "Basic_2/unfold/gr2_gr2.ma".
 include "Basic_2/unfold/lifts_lift_vector.ma".
+include "Basic_2/unfold/ldrops_ldrop.ma".
 include "Basic_2/computation/acp.ma".
 
 (* ABSTRACT COMPUTATION PROPERTIES ******************************************)
@@ -25,25 +27,25 @@ definition S1 ≝ λRP,C:lenv→predicate term.
 (* Note: this is Tait's iii, or Girard's CR4 *)
 definition S2 ≝ λRR:lenv→relation term. λRS:relation term. λRP,C:lenv→predicate term.
                 ∀L,Vs. all … (RP L) Vs →
-                ∀T. 𝕊[T] → NF … (RR L) RS T → C L (ⒶVs.T).
+                ∀T. 𝐒[T] → NF … (RR L) RS T → C L (ⒶVs.T).
 
 (* Note: this is Tait's ii *)
 definition S3 ≝ λRP,C:lenv→predicate term.
-                ∀L,Vs,V,T,W. C L (ⒶVs. 𝕔{Abbr}V. T) → RP L W → C L (ⒶVs. 𝕔{Appl}V. 𝕔{Abst}W. T).
+                ∀L,Vs,V,T,W. C L (ⒶVs. ⓓV. T) → RP L W → C L (ⒶVs. ⓐV. ⓛW. T).
 
 definition S4 ≝ λRP,C:lenv→predicate term. ∀L,K,Vs,V1,V2,i.
                 C L (ⒶVs. V2) → ⇧[0, i + 1] V1 ≡ V2 →
-                ⇩[0, i] L ≡ K. 𝕓{Abbr} V1 → C L (Ⓐ Vs. #i).
+                ⇩[0, i] L ≡ K. ⓓV1 → C L (Ⓐ Vs. #i).
 
 definition S5 ≝ λRP,C:lenv→predicate term.
                 ∀L,V1s,V2s. ⇧[0, 1] V1s ≡ V2s →
-                ∀V,T. C (L. 𝕓{Abbr}V) (ⒶV2s. T) → RP L V → C L (ⒶV1s. 𝕔{Abbr}V. T).
+                ∀V,T. C (L. ⓓV) (ⒶV2s. T) → RP L V → C L (ⒶV1s. ⓓV. T).
 
 definition S6 ≝ λRP,C:lenv→predicate term.
-                ∀L,Vs,T,W. C L (ⒶVs. T) → RP L W → C L (ⒶVs. 𝕔{Cast}W. T).
+                ∀L,Vs,T,W. C L (ⒶVs. T) → RP L W → C L (ⒶVs. ⓣW. T).
 
-definition S7 ≝ λC:lenv→predicate term. ∀L1,L2,T1,T2,d,e.
-                C L1 T1 → ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → C L2 T2.
+definition S7 ≝ λC:lenv→predicate term. ∀L2,L1,T1,d,e.
+                C L1 T1 → ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → C L2 T2.
 
 definition S7s ≝ λC:lenv→predicate term.
                  ∀L1,L2,des. ⇩*[des] L2 ≡ L1 →
@@ -65,7 +67,7 @@ let rec aacr (RP:lenv→predicate term) (A:aarity) (L:lenv) on A: predicate term
 λT. match A with
 [ AAtom     ⇒ RP L T
 | APair B A ⇒ ∀L0,V0,T0,des. aacr RP B L0 V0 → ⇩*[des] L0 ≡ L → ⇧*[des] T ≡ T0 →
-              aacr RP A L0 (𝕔{Appl} V0. T0)
+              aacr RP A L0 (ⓐV0. T0)
 ].
 
 interpretation
@@ -74,6 +76,7 @@ interpretation
 
 (* Basic properties *********************************************************)
 
+(* Basic_1: was: sc3_lift1 *)
 lemma acr_lifts: ∀C. S7 C → S7s C.
 #C #HC #L1 #L2 #des #H elim H -L1 -L2 -des
 [ #L #T1 #T2 #H #HT1
@@ -91,17 +94,20 @@ lemma rp_lifts: ∀RR,RS,RP. acr RR RS RP (λL,T. RP L T) →
 @(s7 … HRP)
 qed.
 
+(* Basic_1: was only: sns3_lifts1 *)
 lemma rp_liftsv_all: ∀RR,RS,RP. acr RR RS RP (λL,T. RP L T) →
-                     ∀des,L0,L,Vs,V0s. ⇧*[des] Vs ≡ V0s →  ⇩*[des] L0 ≡ L →
+                     ∀des,L0,L,Vs,V0s. ⇧*[des] Vs ≡ V0s → ⇩*[des] L0 ≡ L →
                      all … (RP L) Vs → all … (RP L0) V0s.
 #RR #RS #RP #HRP #des #L0 #L #Vs #V0s #H elim H -Vs -V0s normalize //
 #T1s #T2s #T1 #T2 #HT12 #_ #IHT2s #HL0 * #HT1 #HT1s
 @conj /2 width=1/ /2 width=6 by rp_lifts/
 qed.
 
-axiom aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
+(* Basic_1: was: 
+   sc3_sn3 sc3_abst sc3_appl sc3_abbr sc3_bind sc3_cast sc3_lift
+*) 
+lemma aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
                 ∀A. acr RR RS RP (aacr RP A).
-(*
 #RR #RS #RP #H1RP #H2RP #A elim A -A normalize //
 #B #A #IHB #IHA @mk_acr normalize
 [ #L #T #H
@@ -119,6 +125,16 @@ axiom aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
   elim (lifts_inv_flat1 … HY) -HY #U0 #X #HU0 #HX #H destruct
   elim (lifts_inv_bind1 … HX) -HX #W0 #T0 #HW0 #HT0 #H destruct
   @(s3 … IHA … (V0 :: V0s)) /2 width=6 by rp_lifts/ /4 width=5/
+| #L #K #Vs #V1 #V2 #i #HA #HV12 #HLK #L0 #V0 #X #des #HB #HL0 #H
+  elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
+  elim (lifts_inv_lref1 … HY) -HY #i0 #Hi0 #H destruct
+  elim (ldrops_ldrop_trans … HL0 … HLK) #X #des0 #i1 #HL02 #H #Hi1 #Hdes0
+  >(at_mono … Hi1 … Hi0) in HL02; -i1 #HL02
+  elim (ldrops_inv_skip2 … Hdes0 … H) -H -des0 #L2 #W1 #des0 #Hdes0 #HLK #HVW1 #H destruct
+  elim (lift_total W1 0 (i0 + 1)) #W2 #HW12
+  elim (lifts_lift_trans  … Hdes0 … HVW1 … HW12) // -Hdes0 -Hi0 #V3 #HV13 #HVW2
+  >(lift_mono … HV13 … HV12) in HVW2; -V3 #HVW2
+  @(s4 … IHA … (V0 :: V0s) … HW12 HL02) /3 width=4/
 | #L #V1s #V2s #HV12s #V #T #HA #HV #L0 #V10 #X #des #HB #HL0 #H
   elim (lifts_inv_applv1 … H) -H #V10s #Y #HV10s #HY #H destruct
   elim (lifts_inv_bind1 … HY) -HY #V0 #T0 #HV0 #HT0 #H destruct
@@ -127,7 +143,7 @@ axiom aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
   @(s5 … IHA … (V10 :: V10s) (V20 :: V20s)) /2 width=1/ /2 width=6 by rp_lifts/
   @(HA … (des + 1)) /2 width=1/
   [ @(s7 … IHB … HB … HV120) /2 width=1/
-  | @liftsv_applv //
+  | @lifts_applv //
     elim (liftsv_liftv_trans_le … HV10s … HV120s) -V10s #V10s #HV10s #HV120s
     >(liftv_mono … HV12s … HV10s) -V1s //
   ]
@@ -138,13 +154,13 @@ axiom aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
 | /3 width=7/
 ]
 qed.
-*)
+
 lemma aacr_abst: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
                  ∀L,W,T,A,B. RP L W → (
                     ∀L0,V0,T0,des. ⇩*[des] L0 ≡ L → ⇧*[des + 1] T ≡ T0 →
-                                   ⦃L0, V0⦄ [RP] ϵ 〚B〛 → ⦃L0. 𝕓{Abbr} V0, T0⦄ [RP] ϵ 〚A〛
+                                   ⦃L0, V0⦄ [RP] ϵ 〚B〛 → ⦃L0. ⓓV0, T0⦄ [RP] ϵ 〚A〛
                  ) →
-                 ⦃L, 𝕓{Abst} W. T⦄ [RP] ϵ 〚𝕔 B. A〛.
+                 ⦃L, ⓛW. T⦄ [RP] ϵ 〚②B. A〛.
 #RR #RS #RP #H1RP #H2RP #L #W #T #A #B #HW #HA #L0 #V0 #X #des #HB #HL0 #H
 lapply (aacr_acr … H1RP H2RP A) #HCA
 lapply (aacr_acr … H1RP H2RP B) #HCB
@@ -153,3 +169,6 @@ lapply (s1 … HCB) -HCB #HCB
 @(s3 … HCA … ◊) /2 width=6 by rp_lifts/
 @(s5 … HCA … ◊ ◊) // /2 width=1/ /2 width=3/
 qed.
+
+(* Basic_1: removed theorems 2: sc3_arity_gen sc3_repl *)
+(* Basic_1: removed local theorems 1: sc3_sn3_abst *)