- some renaming according to the written version of basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/gcp_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/gcp_aaa.ma
index c890be39ea877839ae6e80dc20c60cdbc686ef2d..6ff7ee8048248ee35c853c426a352ba60933df81 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/gcp_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/gcp_aaa.ma
@@ -25,50 +25,50 @@ include "basic_2/computation/lsubc_drops.ma".
 (* Basic_1: was: sc3_arity_csubc *)
 theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
                              gcp RR RS RP → gcr RR RS RP RP →
-                             â\88\80G,L1,T,A. â¦\83G, L1â¦\84 â\8a¢ T â\81\9d A â\86\92 â\88\80L0,des. â\87©*[Ⓕ, des] L0 ≡ L1 →
-                             â\88\80T0. â\87§*[des] T ≡ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
+                             â\88\80G,L1,T,A. â¦\83G, L1â¦\84 â\8a¢ T â\81\9d A â\86\92 â\88\80L0,des. â¬\87*[Ⓕ, des] L0 ≡ L1 →
+                             â\88\80T0. â¬\86*[des] T ≡ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
                              ⦃G, L2, T0⦄ ϵ[RP] 〚A〛.
 #RR #RS #RP #H1RP #H2RP #G #L1 #T #A #H elim H -G -L1 -T -A
 [ #G #L #k #L0 #des #HL0 #X #H #L2 #HL20
   >(lifts_inv_sort1 … H) -H
   lapply (acr_gcr … H1RP H2RP (⓪)) #HAtom
-  @(s4 … HAtom … (◊)) //
+  lapply (s4 … HAtom G L2 (◊)) /2 width=1 by/
 | #I #G #L1 #K1 #V1 #B #i #HLK1 #HKV1B #IHB #L0 #des #HL01 #X #H #L2 #HL20
   lapply (acr_gcr … H1RP H2RP B) #HB
   elim (lifts_inv_lref1 … H) -H #i1 #Hi1 #H destruct
   lapply (drop_fwd_drop2 … HLK1) #HK1b
-  elim (drops_drop_trans … HL01 … HLK1) #X #des1 #i0 #HL0 #H #Hi0 #Hdes1
+  elim (drops_drop_trans … HL01 … HLK1) #X #des1 #i0 #HL0 #H #Hi0 #Hcs1
   >(at_mono … Hi1 … Hi0) -i1
-  elim (drops_inv_skip2 … Hdes1 … H) -des1 #K0 #V0 #des0 #Hdes0 #HK01 #HV10 #H destruct
+  elim (drops_inv_skip2 … Hcs1 … H) -des1 #K0 #V0 #des0 #Hcs0 #HK01 #HV10 #H destruct
   elim (lsubc_drop_O1_trans … HL20 … HL0) -HL0 #X #HLK2 #H
   elim (lsubc_inv_pair2 … H) -H *
   [ #K2 #HK20 #H destruct
     elim (lift_total V0 0 (i0 +1)) #V #HV0
-    elim (lifts_lift_trans  … Hi0 … Hdes0 … HV10 … HV0) -HV10 #V2 #HV12 #HV2
-    @(s5 … HB … (◊) … HV0 HLK2) /3 width=7 by drops_cons, lifts_cons/ (* Note: uses IHB HL20 V2 HV0 *)
-  | -HLK1 -IHB -HL01 -HL20 -HK1b -Hi0 -Hdes0
+    elim (lifts_lift_trans  … Hi0 … Hcs0 … HV10 … HV0) -HV10 #V2 #HV12 #HV2
+    lapply (s5 … HB ? G ? ? (◊) … HV0 HLK2) /3 width=7 by drops_cons, lifts_cons/ (* Note: uses IHB HL20 V2 HV0 *)
+  | -HLK1 -IHB -HL01 -HL20 -HK1b -Hi0 -Hcs0
     #K2 #V2 #A2 #HKV2A #H1KV0A #H2KV0A #_ #H1 #H2 destruct
     lapply (drop_fwd_drop2 … HLK2) #HLK2b
     lapply (aaa_lifts … HK01 … HV10 HKV1B) -HKV1B -HK01 -HV10 #HKV0B
     lapply (aaa_mono … H2KV0A … HKV0B) #H destruct -H2KV0A -HKV0B
     elim (lift_total V0 0 (i0 +1)) #V3 #HV03
     elim (lift_total V2 0 (i0 +1)) #V #HV2
-    @(s5 … HB … (◊) … (ⓝV3.V) … HLK2) [2: /2 width=1 by lift_flat/ ]
-    @(s7 … HB … (◊)) [ @(s0 … HB … HKV2A) // | @(s0 … HB … H1KV0A) // ]
+    lapply (s5 … HB ? G ? ? (◊) … (ⓝV3.V) … HLK2) /2 width=1 by lift_flat/
+    lapply (s7 … HB G L2 (◊)) /3 width=7 by gcr_lift/
   ]
 | #a #G #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 (acr_gcr … H1RP H2RP A) #HA
   lapply (acr_gcr … H1RP H2RP B) #HB
   lapply (s1 … HB) -HB #HB
-  @(s6 … HA … (◊) (◊)) /3 width=5 by lsubc_pair, drops_skip, liftv_nil/
+  lapply (s6 … HA G L2 (◊) (◊)) /4 width=5 by lsubc_pair, drops_skip, liftv_nil/
 | #a #G #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
-  @(acr_abst  … H1RP H2RP) [ /2 width=5 by/ ]
+  @(acr_abst  … H1RP H2RP) /2 width=5 by/
   #L3 #V3 #W3 #T3 #des3 #HL32 #HW03 #HT03 #H1B #H2B
-  elim (drops_lsubc_trans … H1RP H2RP … HL32 … HL02) -L2 #L2 #HL32 #HL20
+  elim (drops_lsubc_trans … H1RP … HL32 … HL02) -L2 #L2 #HL32 #HL20
   lapply (aaa_lifts … L2 W3 … (des @@ des3) … HLWB) -HLWB /2 width=4 by drops_trans, lifts_trans/ #HLW2B
-  @(IHA (L2. ⓛW3) … (des + 1 @@ des3 + 1)) -IHA 
+  @(IHA (L2. ⓛW3) … (des + 1 @@ des3 + 1)) -IHA
   /3 width=5 by lsubc_beta, drops_trans, drops_skip, lifts_trans/
 | #G #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
@@ -76,7 +76,7 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
 | #G #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 (acr_gcr … H1RP H2RP A) #HA
-  @(s7 … HA … (◊)) /2 width=5 by/
+  lapply (s7 … HA G L2 (◊)) /3 width=5 by/
 ]
 qed.