- xoa: the definitions file now includes the notations file

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/acp_cr.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/acp_cr.ma
index 482349b69d8aa73cb31986b3ebcc0cb44a465d09..1b0d56c7cd4948fe0cfb798e5d3fe012887d6c5b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/acp_cr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/acp_cr.ma
@@ -89,7 +89,7 @@ lemma acr_lifts: ∀C. S8 C → S8s C.
 [ #L #T1 #T2 #H #HT1
   <(lifts_inv_nil … H) -H //
 | #L1 #L #L2 #des #d #e #_ #HL2 #IHL #T2 #T1 #H #HLT2
-  elim (lifts_inv_cons … H) -H /3 width=9/
+  elim (lifts_inv_cons … H) -H /3 width=9 by/
 ]
 qed.
 
@@ -97,7 +97,7 @@ lemma rp_lifts: ∀RR,RS,RP. acr RR RS RP (λG,L,T. RP G L T) →
                 ∀des,G,L0,L,V,V0. ⇩*[des] L0 ≡ L → ⇧*[des] V ≡ V0 →
                 RP G L V → RP G L0 V0.
 #RR #RS #RP #HRP #des #G #L0 #L #V #V0 #HL0 #HV0 #HV
-@acr_lifts /width=6/
+@acr_lifts /width=6 by/
 @(s8 … HRP)
 qed.
 
@@ -106,8 +106,7 @@ lemma rp_liftsv_all: ∀RR,RS,RP. acr RR RS RP (λG,L,T. RP G L T) →
                      ∀des,G,L0,L,Vs,V0s. ⇧*[des] Vs ≡ V0s → ⇩*[des] L0 ≡ L →
                      all … (RP G L) Vs → all … (RP G L0) V0s.
 #RR #RS #RP #HRP #des #G #L0 #L #Vs #V0s #H elim H -Vs -V0s normalize //
-#T1s #T2s #T1 #T2 #HT12 #_ #IHT2s #HL0 * #HT1 #HT1s
-@conj /2 width=1/ /2 width=6 by rp_lifts/
+#T1s #T2s #T1 #T2 #HT12 #_ #IHT2s #HL0 * /3 width=6 by rp_lifts, conj/
 qed.
 
 (* Basic_1: was:
@@ -119,25 +118,26 @@ lemma aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) 
 #B #A #IHB #IHA @mk_acr normalize
 [ #G #L #T #H
   elim (cp1 … H1RP G L) #k #HK
-  lapply (H ? (⋆k) ? ⟠ ? ? ?) -H
+  lapply (H ? (⋆k) ? (⟠) ? ? ?) -H
   [1,3: // |2,4: skip
-  | @(s2 … IHB … ◊) //
+  | @(s2 … IHB … (◊)) //
   | #H @(cp3 … H1RP … k) @(s1 … IHA) //
   ]
 | #G #L #Vs #HVs #T #H1T #H2T #L0 #V0 #X #des #HB #HL0 #H
   elim (lifts_inv_applv1 … H) -H #V0s #T0 #HV0s #HT0 #H destruct
   lapply (s1 … IHB … HB) #HV0
-  @(s2 … IHA … (V0 @ V0s)) /2 width=4 by lifts_simple_dx/ /3 width=6/
+  @(s2 … IHA … (V0 @ V0s))
+  /3 width=13 by rp_liftsv_all, acp_lifts, cp2, lifts_simple_dx, conj/
 | #a #G #L #Vs #U #T #W #HA #L0 #V0 #X #des #HB #HL0 #H
   elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
   elim (lifts_inv_flat1 … HY) -HY #U0 #X #HU0 #HX #H destruct
   elim (lifts_inv_bind1 … HX) -HX #W0 #T0 #HW0 #HT0 #H destruct
-  @(s3 … IHA … (V0 @ V0s)) /5 width=5/
+  @(s3 … IHA … (V0 @ V0s)) /5 width=5 by lifts_applv, lifts_flat, lifts_bind/
 | #G #L #Vs #HVs #k #L0 #V0 #X #hdes #HB #HL0 #H
   elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
   >(lifts_inv_sort1 … HY) -Y
   lapply (s1 … IHB … HB) #HV0
-  @(s4 … IHA … (V0 @ V0s)) /3 width=6/
+  @(s4 … IHA … (V0 @ V0s)) /3 width=6 by rp_liftsv_all, conj/
 | #I #G #L #K #Vs #V1 #V2 #i #HA #HV12 #HLK #L0 #V0 #X #des #HB #HL0 #H
   elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
   elim (lifts_inv_lref1 … HY) -HY #i0 #Hi0 #H destruct
@@ -147,15 +147,15 @@ lemma aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) 
   elim (lift_total W1 0 (i0 + 1)) #W2 #HW12
   elim (lifts_lift_trans  … Hdes0 … HVW1 … HW12) // -Hdes0 -Hi0 #V3 #HV13 #HVW2
   >(lift_mono … HV13 … HV12) in HVW2; -V3 #HVW2
-  @(s5 … IHA … (V0 @ V0s) … HW12 HL02) /3 width=4/
+  @(s5 … IHA … (V0 @ V0s) … HW12 HL02) /3 width=4 by lifts_applv/
 | #G #L #V1s #V2s #HV12s #a #V #T #HA #HV #L0 #V10 #X #des #HB #HL0 #H
   elim (lifts_inv_applv1 … H) -H #V10s #Y #HV10s #HY #H destruct
   elim (lifts_inv_bind1 … HY) -HY #V0 #T0 #HV0 #HT0 #H destruct
   elim (lift_total V10 0 1) #V20 #HV120
   elim (liftv_total 0 1 V10s) #V20s #HV120s
-  @(s6 … IHA … (V10 @ V10s) (V20 @ V20s)) /2 width=1/ /3 width=6 by rp_lifts/
-  @(HA … (des + 1)) /2 width=1/
-  [ @(s8 … IHB … HB … HV120) /2 width=1/
+  @(s6 … IHA … (V10 @ V10s) (V20 @ V20s)) /3 width=6 by rp_lifts, liftv_cons/
+  @(HA … (des + 1)) /2 width=1 by ldrops_skip/
+  [ @(s8 … IHB … HB … HV120) /2 width=1 by ldrop_ldrop/
   | @lifts_applv //
     elim (liftsv_liftv_trans_le … HV10s … HV120s) -V10s #V10s #HV10s #HV120s
     >(liftv_mono … HV12s … HV10s) -V1s //
@@ -163,8 +163,8 @@ lemma aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λG,L,T. RP G L T) 
 | #G #L #Vs #T #W #HA #HW #L0 #V0 #X #des #HB #HL0 #H
   elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
   elim (lifts_inv_flat1 … HY) -HY #W0 #T0 #HW0 #HT0 #H destruct
-  @(s7 … IHA … (V0 @ V0s)) /3 width=4/
-| /3 width=7/
+  @(s7 … IHA … (V0 @ V0s)) /3 width=4 by lifts_applv/
+| /3 width=7 by ldrops_cons, lifts_cons/
 ]
 qed.
 
@@ -179,11 +179,11 @@ lapply (aacr_acr … H1RP H2RP A) #HCA
 lapply (aacr_acr … H1RP H2RP B) #HCB
 elim (lifts_inv_bind1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
 lapply (acr_lifts … HL0 … HW0 HW) -HW [ @(s8 … HCB) ] #HW0
-@(s3 … HCA … ◊)
-@(s6 … HCA … ◊ ◊) //
+@(s3 … HCA … (◊))
+@(s6 … HCA … (◊) (◊)) //
 [ @(HA … HL0) //
 | lapply (s1 … HCB) -HCB #HCB
-  @(cp4 … H1RP) /2 width=1/
+  @(cp4 … H1RP) /2 width=1 by/
 ]
 qed.