partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / gcp_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/gcp_aaa.ma b/matita/matita/contribs/lambdadelta/static_2/static/gcp_aaa.ma
index d1dc57ece3d6f38721e9308849aa6039e6ef95e9..40e757ad62b4c9bd4445c6e82a1cfd5b492ace06 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/gcp_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/gcp_aaa.ma
@@ -20,28 +20,28 @@ include "static_2/static/lsubc_drops.ma".
 (* 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〛.
+theorem acr_aaa_lsubc_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 ⟦A⟧[RP].
 #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/
+  lapply (s2 … HAtom G L2 (Ⓔ)) /3 width=7 by cp1, simple_atom/
 | #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
+  elim (drops_split_trans … H) -H [ |*: /2 width=6 by pr_after_nat_uni/ ] #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 (ð\9d\90\94â\9d´â\86\91jâ\9dµ)) #V #HV0
+  elim (lifts_total V0 (ð\9d\90\94â\9d¨â\86\91jâ\9d©)) #V #HV0
   elim (lsubc_drops_trans_isuni … HL20 … HLK0) -HL20 -HLK0 // #Y #HLK2 #H
   elim (lsubc_inv_bind2 … H) -H *
   [ #K2 #HK20 #H destruct
@@ -52,7 +52,7 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
     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 (ð\9d\90\94â\9d´â\86\91jâ\9dµ)) #V3 #HV23
+    elim (lifts_total V2 (ð\9d\90\94â\9d¨â\86\91jâ\9d©)) #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/
@@ -90,12 +90,14 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
 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 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 ⟦A⟧[RP].
+/3 width=9 by drops_refl, lifts_refl, acr_aaa_lsubc_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.
+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/