- predefined_virtuals: some additions

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/acp_cr.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/acp_cr.ma
index c300d19de779e4283014d3a3118b076b9db8fa3e..5b8a2c1ea3652235976d2e5c5665d03a704ed3cb 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/computation/acp_cr.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/computation/acp_cr.ma
@@ -27,7 +27,7 @@ definition S1 ≝ λRP,C:lenv→predicate term.
 (* Note: this is Tait's iii, or Girard's CR4 *)
 definition S2 ≝ λRR:lenv→relation term. λRS:relation term. λRP,C:lenv→predicate term.
                 ∀L,Vs. all … (RP L) Vs →
-                ∀T. 𝐒[T] → NF … (RR L) RS T → C L (ⒶVs.T).
+                ∀T. 𝐒⦃T⦄ → NF … (RR L) RS T → C L (ⒶVs.T).
 
 (* Note: this is Tait's ii *)
 definition S3 ≝ λRP,C:lenv→predicate term.
@@ -42,7 +42,7 @@ definition S5 ≝ λRP,C:lenv→predicate term.
                 ∀V,T. C (L. ⓓV) (ⒶV2s. T) → RP L V → C L (ⒶV1s. ⓓV. T).
 
 definition S6 ≝ λRP,C:lenv→predicate term.
-                â\88\80L,Vs,T,W. C L (â\92¶Vs. T) â\86\92 RP L W â\86\92 C L (â\92¶Vs. â\93£W. T).
+                â\88\80L,Vs,T,W. C L (â\92¶Vs. T) â\86\92 RP L W â\86\92 C L (â\92¶Vs. â\93\9dW. T).
 
 definition S7 ≝ λC:lenv→predicate term. ∀L2,L1,T1,d,e.
                 C L1 T1 → ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → C L2 T2.
@@ -119,12 +119,12 @@ lemma aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
 | #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)) /2 width=4 by lifts_simple_dx/ /3 width=6/
 | #L #Vs #U #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 #U0 #X #HU0 #HX #H destruct
   elim (lifts_inv_bind1 … HX) -HX #W0 #T0 #HW0 #HT0 #H destruct
-  @(s3 … IHA … (V0 :: V0s)) /2 width=6 by rp_lifts/ /4 width=5/
+  @(s3 … IHA … (V0 @ V0s)) /2 width=6 by rp_lifts/ /4 width=5/
 | #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
@@ -134,13 +134,13 @@ lemma aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP 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
-  @(s4 … IHA … (V0 :: V0s) … HW12 HL02) /3 width=4/
+  @(s4 … IHA … (V0 @ V0s) … HW12 HL02) /3 width=4/
 | #L #V1s #V2s #HV12s #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
-  @(s5 … IHA … (V10 :: V10s) (V20 :: V20s)) /2 width=1/ /2 width=6 by rp_lifts/
+  @(s5 … IHA … (V10 @ V10s) (V20 @ V20s)) /2 width=1/ /2 width=6 by rp_lifts/
   @(HA … (des + 1)) /2 width=1/
   [ @(s7 … IHB … HB … HV120) /2 width=1/
   | @lifts_applv //
@@ -150,7 +150,7 @@ lemma aacr_acr: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
 | #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
-  @(s6 … IHA … (V0 :: V0s)) /2 width=6 by rp_lifts/ /3 width=4/
+  @(s6 … IHA … (V0 @ V0s)) /2 width=6 by rp_lifts/ /3 width=4/
 | /3 width=7/
 ]
 qed.
@@ -158,9 +158,9 @@ qed.
 lemma aacr_abst: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
                  ∀L,W,T,A,B. RP L W → (
                     ∀L0,V0,T0,des. ⇩*[des] L0 ≡ L → ⇧*[des + 1] T ≡ T0 →
-                                   ⦃L0, V0⦄ [RP] ϵ 〚B〛 → ⦃L0. ⓓV0, T0⦄ [RP] ϵ 〚A〛
+                                   ⦃L0, V0⦄ ϵ[RP] 〚B〛 → ⦃L0. ⓓV0, T0⦄ ϵ[RP] 〚A〛
                  ) →
-                 ⦃L, ⓛW. T⦄ [RP] ϵ 〚②B. A〛.
+                 ⦃L, ⓛW. T⦄ ϵ[RP] 〚②B. A〛.
 #RR #RS #RP #H1RP #H2RP #L #W #T #A #B #HW #HA #L0 #V0 #X #des #HB #HL0 #H
 lapply (aacr_acr … H1RP H2RP A) #HCA
 lapply (aacr_acr … H1RP H2RP B) #HCB