- the trace is explicit in all auto tactics with depth > 1

[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 6ff7ee8048248ee35c853c426a352ba60933df81..3428478ea0cc3fc7bb7f2d826d4d3a37ad9215ee 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/gcp_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/gcp_aaa.ma
@@ -25,21 +25,21 @@ 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 →
-                             ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀L0,des. ⬇*[Ⓕ, des] L0 ≡ L1 →
-                             ∀T0. ⬆*[des] T ≡ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
+                             ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀L0,cs. ⬇*[Ⓕ, cs] L0 ≡ L1 →
+                             ∀T0. ⬆*[cs] 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
+[ #G #L #k #L0 #cs #HL0 #X #H #L2 #HL20
   >(lifts_inv_sort1 … H) -H
   lapply (acr_gcr … H1RP H2RP (⓪)) #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
+| #I #G #L1 #K1 #V1 #B #i #HLK1 #HKV1B #IHB #L0 #cs #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 #Hcs1
+  elim (drops_drop_trans … HL01 … HLK1) #X #cs1 #i0 #HL0 #H #Hi0 #Hcs1
   >(at_mono … Hi1 … Hi0) -i1
-  elim (drops_inv_skip2 … Hcs1 … H) -des1 #K0 #V0 #des0 #Hcs0 #HK01 #HV10 #H destruct
+  elim (drops_inv_skip2 … Hcs1 … H) -cs1 #K0 #V0 #cs0 #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
@@ -56,24 +56,24 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
     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
+| #a #G #L #V #T #B #A #_ #_ #IHB #IHA #L0 #cs #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
   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
+| #a #G #L #W #T #B #A #HLWB #_ #IHB #IHA #L0 #cs #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/
-  #L3 #V3 #W3 #T3 #des3 #HL32 #HW03 #HT03 #H1B #H2B
+  #L3 #V3 #W3 #T3 #cs3 #HL32 #HW03 #HT03 #H1B #H2B
   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
+  lapply (aaa_lifts … L2 W3 … (cs @@ cs3) … HLWB) -HLWB /2 width=4 by drops_trans, lifts_trans/ #HLW2B
+  @(IHA (L2. ⓛW3) … (cs + 1 @@ cs3 + 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
+| #G #L #V #T #B #A #_ #_ #IHB #IHA #L0 #cs #HL0 #X #H #L2 #HL20
   elim (lifts_inv_flat1 … H) -H #V0 #T0 #HV0 #HT0 #H destruct
   /3 width=10 by drops_nil, lifts_nil/
-| #G #L #V #T #A #_ #_ #IH1A #IH2A #L0 #des #HL0 #X #H #L2 #HL20
+| #G #L #V #T #A #_ #_ #IH1A #IH2A #L0 #cs #HL0 #X #H #L2 #HL20
   elim (lifts_inv_flat1 … H) -H #V0 #T0 #HV0 #HT0 #H destruct
   lapply (acr_gcr … H1RP H2RP A) #HA
   lapply (s7 … HA G L2 (◊)) /3 width=5 by/