- we set up the support for the "bt-reduction" of Automath literature

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / computation / acp_aaa.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/acp_aaa.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/acp_aaa.ma
index 1cab5d4b8f2b2a04c143d648dc3e190375732165..f4da11310f6e055a168f11605d84f7a1701344bb 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/acp_aaa.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/acp_aaa.ma
@@ -12,11 +12,11 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic_2/unfold/lifts_lifts.ma".
-include "Basic_2/unfold/ldrops_ldrops.ma".
-include "Basic_2/static/aaa_lifts.ma".
-include "Basic_2/static/aaa_aaa.ma".
-include "Basic_2/computation/lsubc_ldrops.ma".
+include "basic_2/unfold/lifts_lifts.ma".
+include "basic_2/unfold/ldrops_ldrops.ma".
+include "basic_2/static/aaa_lifts.ma".
+include "basic_2/static/aaa_aaa.ma".
+include "basic_2/computation/lsubc_ldrops.ma".
 
 (* ABSTRACT COMPUTATION PROPERTIES ******************************************)
 
@@ -25,9 +25,9 @@ include "Basic_2/computation/lsubc_ldrops.ma".
 (* Basic_1: was: sc3_arity_csubc *)
 theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
                               acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
-                              ∀L1,T,A. L1 ⊢ T ÷ A → ∀L0,des. ⇩*[des] L0 ≡ L1 →
-                              ∀T0. ⇧*[des] T ≡ T0 → ∀L2. L2 [RP] ⊑ L0 →
-                              ⦃L2, T0⦄ [RP] ϵ 〚A〛.
+                              ∀L1,T,A. L1 ⊢ T ⁝ A → ∀L0,des. ⇩*[des] L0 ≡ L1 →
+                              ∀T0. ⇧*[des] T ≡ T0 → ∀L2. L2 ⊑[RP] L0 →
+                              ⦃L2, T0⦄ ϵ[RP] 〚A〛.
 #RR #RS #RP #H1RP #H2RP #L1 #T #A #H elim H -L1 -T -A
 [ #L #k #L0 #des #HL0 #X #H #L2 #HL20
   >(lifts_inv_sort1 … H) -H
@@ -58,13 +58,13 @@ theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
     @(s4 … HB … ◊ … HV2 HLK2)
     @(s7 … HB … HKV2B) //
   ]
-| #L #V #T #B #A #_ #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL20
+| #a #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 (aacr_acr … H1RP H2RP A) #HA
   lapply (aacr_acr … H1RP H2RP B) #HB
   lapply (s1 … HB) -HB #HB
   @(s5 … HA … ◊ ◊) // /3 width=5/
-| #L #W #T #B #A #HLWB #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL02
+| #a #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
   @(aacr_abst  … H1RP H2RP)
   [ lapply (aacr_acr … H1RP H2RP B) #HB
@@ -73,8 +73,8 @@ theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
     #L3 #V3 #T3 #des3 #HL32 #HT03 #HB
     elim (lifts_total des3 W0) #W2 #HW02
     elim (ldrops_lsubc_trans … H1RP H2RP … HL32 … HL02) -L2 #L2 #HL32 #HL20
-    lapply (aaa_lifts … L2 W2 … (des @ des3) … HLWB) -HLWB /2 width=3/ #HLW2B
-    @(IHA (L2. ⓛW2) … (des + 1 @ des3 + 1)) -IHA
+    lapply (aaa_lifts … L2 W2 … (des @@ des3) … HLWB) -HLWB /2 width=3/ #HLW2B
+    @(IHA (L2. ⓛW2) … (des + 1 @@ des3 + 1)) -IHA
     /2 width=3/ /3 width=5/
   ]
 | #L #V #T #B #A #_ #_ #IHB #IHA #L0 #des #HL0 #X #H #L2 #HL20
@@ -90,11 +90,11 @@ qed.
 
 (* Basic_1: was: sc3_arity *)
 lemma aacr_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
-                ∀L,T,A. L ⊢ T ÷ A → ⦃L, T⦄ [RP] ϵ 〚A〛.
+                ∀L,T,A. L ⊢ T ⁝ A → ⦃L, T⦄ ϵ[RP] 〚A〛.
 /2 width=8/ qed.
 
 lemma acp_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
-               ∀L,T,A. L ⊢ T ÷ A → RP L T.
+               ∀L,T,A. L ⊢ T ⁝ A → RP L T.
 #RR #RS #RP #H1RP #H2RP #L #T #A #HT
 lapply (aacr_acr … H1RP H2RP A) #HA
 @(s1 … HA) /2 width=4/