- xoa: the definitions file now includes the notations file

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/acp_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/acp_aaa.ma
index 13d69acd47b067ccfa9ee917b75b874c3bbc61d9..3656d36f66f42ec22e293262756ae6d41c85faa2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/acp_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/acp_aaa.ma
@@ -32,7 +32,7 @@ theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
 [ #G #L #k #L0 #des #HL0 #X #H #L2 #HL20
   >(lifts_inv_sort1 … H) -H
   lapply (aacr_acr … H1RP H2RP (⓪)) #HAtom
-  @(s4 … HAtom … ◊) //
+  @(s4 … HAtom … (◊)) //
 | #I #G #L1 #K1 #V1 #B #i #HLK1 #HKV1B #IHB #L0 #des #HL01 #X #H #L2 #HL20
   lapply (aacr_acr … H1RP H2RP B) #HB
   elim (lifts_inv_lref1 … H) -H #i1 #Hi1 #H destruct
@@ -45,7 +45,7 @@ theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
   [ #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/ (* uses IHB HL20 V2 HV0 *)
+    @(s5 … HB … (◊) … HV0 HLK2) /3 width=7 by ldrops_cons, lifts_cons/ (* Note: uses IHB HL20 V2 HV0 *)
   | -HLK1 -IHB -HL01 -HL20 -HK1b -Hi0 -Hdes0
     #K2 #V2 #A2 #HKV2A #H1KV0A #H2KV0A #_ #H1 #H2 destruct
     lapply (ldrop_fwd_ldrop2 … HLK2) #HLK2b
@@ -53,40 +53,40 @@ theorem aacr_aaa_csubc_lifts: ∀RR,RS,RP.
     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/ ]
-    @(s7 … HB … ◊) [ @(s8 … HB … HKV2A) // | @(s8 … HB … H1KV0A) // ]
+    @(s5 … HB … (◊) … (ⓝV3.V) … HLK2) [2: /2 width=1 by lift_flat/ ]
+    @(s7 … HB … (◊)) [ @(s8 … HB … HKV2A) // | @(s8 … HB … H1KV0A) // ]
   ]
 | #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 (aacr_acr … H1RP H2RP A) #HA
   lapply (aacr_acr … H1RP H2RP B) #HB
   lapply (s1 … HB) -HB #HB
-  @(s6 … HA … ◊ ◊) // /3 width=5/
+  @(s6 … HA … (◊) (◊)) /3 width=5 by lsubc_pair, ldrops_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
-  @(aacr_abst  … H1RP H2RP) [ /2 width=5/ ]
+  @(aacr_abst  … H1RP H2RP) [ /2 width=5 by/ ]
   #L3 #V3 #W3 #T3 #des3 #HL32 #HW03 #HT03 #H1B #H2B
   elim (ldrops_lsubc_trans … H1RP H2RP … HL32 … HL02) -L2 #L2 #HL32 #HL20
-  lapply (aaa_lifts … L2 W3 … (des @@ des3) … HLWB) -HLWB /2 width=3/ #HLW2B
-  @(IHA (L2. ⓛW3) … (des + 1 @@ des3 + 1)) -IHA /2 width=3/ /3 width=5/
+  lapply (aaa_lifts … L2 W3 … (des @@ des3) … HLWB) -HLWB /2 width=3 by ldrops_trans, lifts_trans/ #HLW2B
+  @(IHA (L2. ⓛW3) … (des + 1 @@ des3 + 1)) -IHA /2 width=3/ /3 width=5 by lsubc_abbr, ldrops_trans, ldrops_skip/
 | #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
-  /3 width=10/
+  /3 width=10 by ldrops_nil, lifts_nil/
 | #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 (aacr_acr … H1RP H2RP A) #HA
-  @(s7 … HA … ◊) /2 width=5/
+  @(s7 … HA … (◊)) /2 width=5 by/
 ]
 qed.
 
 (* Basic_1: was: sc3_arity *)
 lemma aacr_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
                 ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L, T⦄ ϵ[RP] 〚A〛.
-/2 width=8/ qed.
+/2 width=8 by ldrops_nil, lifts_nil, aacr_aaa_csubc_lifts/ qed.
 
 lemma acp_aaa: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) →
                ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → RP G L T.
 #RR #RS #RP #H1RP #H2RP #G #L #T #A #HT
 lapply (aacr_acr … H1RP H2RP A) #HA
-@(s1 … HA) /2 width=4/
+@(s1 … HA) /2 width=4 by aacr_aaa/
 qed.