- probe: critical bug fixed (all objects were deleted due to wrong test)

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / lpr_lpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_lpr.ma
index f9a63718a5d6ed6f04e18d26d0fb2d04b9855de3..d87242057746f55d301151d003e34067b2c52b31 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_lpr.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/grammar/lpx_sn_lpx_sn.ma".
-include "basic_2/relocation/fsup.ma".
+include "basic_2/substitution/fsupp.ma".
 include "basic_2/reduction/lpr_ldrop.ma".
 
 (* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
@@ -26,7 +26,7 @@ fact cpr_conf_lpr_atom_atom:
 
 fact cpr_conf_lpr_atom_delta:
    ∀L0,i. (
-      ∀L,T.♯{L, T} < ♯{L0, #i} →
+      ∀L,T. ⦃L0, #i⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -41,7 +41,7 @@ elim (lpr_inv_pair1 … H1) -H1 #K1 #V1 #HK01 #HV01 #H destruct
 elim (lpr_ldrop_conf … HLK0 … HL02) -HL02 #X2 #H2 #HLK2
 elim (lpr_inv_pair1 … H2) -H2 #K2 #W2 #HK02 #_ #H destruct
 lapply (ldrop_fwd_ldrop2 … HLK2) -W2 #HLK2
-lapply (ldrop_pair2_fwd_fw … HLK0 (#i)) -HLK0 #HLK0
+lapply (fsupp_lref … HLK0) -HLK0 #HLK0
 elim (IH … HLK0 … HV01 … HV02 … HK01 … HK02) -L0 -K0 -V0 #V #HV1 #HV2
 elim (lift_total V 0 (i+1)) #T #HVT
 lapply (cpr_lift … HV2 … HLK2 … HVT2 … HVT) -K2 -V2 /3 width=6/
@@ -50,7 +50,7 @@ qed-.
 (* Basic_1: includes: pr0_delta_delta pr2_delta_delta *)
 fact cpr_conf_lpr_delta_delta:
    ∀L0,i. (
-      ∀L,T.♯{L, T} < ♯{L0, #i} →
+      ∀L,T. ⦃L0, #i⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -70,7 +70,7 @@ lapply (ldrop_fwd_ldrop2 … HLK1) -W1 #HLK1
 elim (lpr_ldrop_conf … HLK0 … HL02) -HL02 #X2 #H2 #HLK2
 elim (lpr_inv_pair1 … H2) -H2 #K2 #W2 #HK02 #_ #H destruct
 lapply (ldrop_fwd_ldrop2 … HLK2) -W2 #HLK2
-lapply (ldrop_pair2_fwd_fw … HLK0 (#i)) -HLK0 #HLK0
+lapply (fsupp_lref … HLK0) -HLK0 #HLK0
 elim (IH … HLK0 … HV01 … HV02 … HK01 … HK02) -L0 -K0 -V0 #V #HV1 #HV2
 elim (lift_total V 0 (i+1)) #T #HVT
 lapply (cpr_lift … HV1 … HLK1 … HVT1 … HVT) -K1 -V1
@@ -79,7 +79,7 @@ qed-.
 
 fact cpr_conf_lpr_bind_bind:
    ∀a,I,L0,V0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓑ{a,I}V0.T0} →
+      ∀L,T. ⦃L0,ⓑ{a,I}V0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -96,7 +96,7 @@ qed-.
 
 fact cpr_conf_lpr_bind_zeta:
    ∀L0,V0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,+ⓓV0.T0} →
+      ∀L,T. ⦃L0,+ⓓV0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -113,7 +113,7 @@ qed-.
 
 fact cpr_conf_lpr_zeta_zeta:
    ∀L0,V0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,+ⓓV0.T0} →
+      ∀L,T. ⦃L0,+ⓓV0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -132,7 +132,7 @@ qed-.
 
 fact cpr_conf_lpr_flat_flat:
    ∀I,L0,V0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓕ{I}V0.T0} →
+      ∀L,T. ⦃L0,ⓕ{I}V0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -149,7 +149,7 @@ qed-.
 
 fact cpr_conf_lpr_flat_tau:
    ∀L0,V0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓝV0.T0} →
+      ∀L,T. ⦃L0,ⓝV0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -164,7 +164,7 @@ qed-.
 
 fact cpr_conf_lpr_tau_tau:
    ∀L0,V0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓝV0.T0} →
+      ∀L,T. ⦃L0,ⓝV0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -179,21 +179,23 @@ qed-.
 
 fact cpr_conf_lpr_flat_beta:
    ∀a,L0,V0,W0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓐV0.ⓛ{a}W0.T0} →
+      ∀L,T. ⦃L0,ⓐV0.ⓛ{a}W0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
    ) →
    ∀V1. L0 ⊢ V0 ➡ V1 → ∀T1. L0 ⊢ ⓛ{a}W0.T0 ➡ T1 →
-   ∀V2. L0 ⊢ V0 ➡ V2 → ∀T2. L0.ⓛW0 ⊢ T0 ➡ T2 →
+   ∀V2. L0 ⊢ V0 ➡ V2 → ∀W2. L0 ⊢ W0 ➡ W2 → ∀T2. L0.ⓛW0 ⊢ T0 ➡ T2 →
    ∀L1. L0 ⊢ ➡ L1 → ∀L2. L0 ⊢ ➡ L2 →
-   ∃∃T. L1 ⊢ ⓐV1.T1 ➡ T & L2 ⊢ ⓓ{a}V2.T2 ➡ T.
+   ∃∃T. L1 ⊢ ⓐV1.T1 ➡ T & L2 ⊢ ⓓ{a}ⓝW2.V2.T2 ➡ T.
 #a #L0 #V0 #W0 #T0 #IH #V1 #HV01 #X #H
-#V2 #HV02 #T2 #HT02 #L1 #HL01 #L2 #HL02
+#V2 #HV02 #W2 #HW02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (cpr_inv_abst1 … H) -H #W1 #T1 #HW01 #HT01 #H destruct
 elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1/ #V #HV1 #HV2
-elim (IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW1)) /2 width=1/ -L0 -V0 -W0 -T0 #T #HT1 #HT2
-lapply (cpr_lsubr_trans … HT2 (L2.ⓓV2) ?) -HT2 /2 width=1/ /3 width=5/
+elim (IH … HW01 … HW02 … HL01 … HL02) /2 width=1/ #W #HW1 #HW2
+elim (IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) /2 width=1/ -L0 -V0 -W0 -T0 #T #HT1 #HT2
+lapply (lsubr_cpr_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1/
+/4 width=5 by cpr_bind, cpr_flat, cpr_beta, ex2_intro/ (**) (* auto too slow without trace *)
 qed-.
 
 (* Basic-1: includes:
@@ -202,7 +204,7 @@ qed-.
 *)
 fact cpr_conf_lpr_flat_theta:
    ∀a,L0,V0,W0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓐV0.ⓓ{a}W0.T0} →
+      ∀L,T. ⦃L0,ⓐV0.ⓓ{a}W0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -231,27 +233,29 @@ qed-.
 
 fact cpr_conf_lpr_beta_beta:
    ∀a,L0,V0,W0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓐV0.ⓛ{a}W0.T0} →
+      ∀L,T. ⦃L0,ⓐV0.ⓛ{a}W0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
    ) →
-   ∀V1. L0 ⊢ V0 ➡ V1 → ∀T1. L0.ⓛW0 ⊢ T0 ➡ T1 →
-   ∀V2. L0 ⊢ V0 ➡ V2 → ∀T2. L0.ⓛW0 ⊢ T0 ➡ T2 →
+   ∀V1. L0 ⊢ V0 ➡ V1 → ∀W1. L0 ⊢ W0 ➡ W1 → ∀T1. L0.ⓛW0 ⊢ T0 ➡ T1 →
+   ∀V2. L0 ⊢ V0 ➡ V2 → ∀W2. L0 ⊢ W0 ➡ W2 → ∀T2. L0.ⓛW0 ⊢ T0 ➡ T2 →
    ∀L1. L0 ⊢ ➡ L1 → ∀L2. L0 ⊢ ➡ L2 →
-   ∃∃T. L1 ⊢ ⓓ{a}V1.T1 ➡ T & L2 ⊢ ⓓ{a}V2.T2 ➡ T.
-#a #L0 #V0 #W0 #T0 #IH #V1 #HV01 #T1 #HT01
-#V2 #HV02 #T2 #HT02 #L1 #HL01 #L2 #HL02
+   ∃∃T. L1 ⊢ ⓓ{a}ⓝW1.V1.T1 ➡ T & L2 ⊢ ⓓ{a}ⓝW2.V2.T2 ➡ T.
+#a #L0 #V0 #W0 #T0 #IH #V1 #HV01 #W1 #HW01 #T1 #HT01
+#V2 #HV02 #W2 #HW02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1/ #V #HV1 #HV2
-elim (IH … HT01 … HT02 (L1.ⓛW0) … (L2.ⓛW0)) /2 width=1/ -L0 -V0 -T0 #T #HT1 #HT2
-lapply (cpr_lsubr_trans … HT1 (L1.ⓓV1) ?) -HT1 /2 width=1/
-lapply (cpr_lsubr_trans … HT2 (L2.ⓓV2) ?) -HT2 /2 width=1/ /3 width=5/
+elim (IH … HW01 … HW02 … HL01 … HL02) /2 width=1/ #W #HW1 #HW2
+elim (IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) /2 width=1/ -L0 -V0 -W0 -T0 #T #HT1 #HT2
+lapply (lsubr_cpr_trans … HT1 (L1.ⓓⓝW1.V1) ?) -HT1 /2 width=1/
+lapply (lsubr_cpr_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1/
+/4 width=5 by cpr_bind, cpr_flat, ex2_intro/
 qed-.
 
 (* Basic_1: was: pr0_upsilon_upsilon *)
 fact cpr_conf_lpr_theta_theta:
    ∀a,L0,V0,W0,T0. (
-      ∀L,T.♯{L,T} < ♯{L0,ⓐV0.ⓓ{a}W0.T0} →
+      ∀L,T. ⦃L0,ⓐV0.ⓓ{a}W0.T0⦄ ⊃+ ⦃L, T⦄ →
       ∀T1. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ➡ T2 →
       ∀L1. L ⊢ ➡ L1 → ∀L2. L ⊢ ➡ L2 →
       ∃∃T0. L1 ⊢ T1 ➡ T0 & L2 ⊢ T2 ➡ T0
@@ -274,8 +278,8 @@ lapply (cpr_lift … HV2 (L2.ⓓW2) … HVU2 … HVU) -HVU2 /2 width=1/
 qed-.
 
 theorem cpr_conf_lpr: lpx_sn_confluent cpr cpr.
-#L0 #T0 @(f2_ind … fw … L0 T0) -L0 -T0 #n #IH #L0 * [|*]
-[ #I0 #Hn #T1 #H1 #T2 #H2 #L1 #HL01 #L2 #HL02 destruct
+#L0 #T0 @(fsupp_wf_ind … L0 T0) -L0 -T0 #L #T #IH #L0 * [|*]
+[ #I0 #HL #HT #T1 #H1 #T2 #H2 #L1 #HL01 #L2 #HL02 destruct
   elim (cpr_inv_atom1 … H1) -H1
   elim (cpr_inv_atom1 … H2) -H2
   [ #H2 #H1 destruct
@@ -288,7 +292,7 @@ theorem cpr_conf_lpr: lpx_sn_confluent cpr cpr.
     * #K0 #V0 #V1 #i #HLK0 #HV01 #HVT1 #H1 destruct
     /3 width=17 by cpr_conf_lpr_delta_delta/
   ]
-| #a #I #V0 #T0 #Hn #X1 #H1 #X2 #H2 #L1 #HL01 #L2 #HL02 destruct
+| #a #I #V0 #T0 #HL #HT #X1 #H1 #X2 #H2 #L1 #HL01 #L2 #HL02 destruct
   elim (cpr_inv_bind1 … H1) -H1 *
   [ #V1 #T1 #HV01 #HT01 #H1
   | #T1 #HT01 #HXT1 #H11 #H12
@@ -302,27 +306,27 @@ theorem cpr_conf_lpr: lpx_sn_confluent cpr cpr.
   | /3 width=11 by cpr_conf_lpr_bind_zeta/
   | /3 width=12 by cpr_conf_lpr_zeta_zeta/
   ]
-| #I #V0 #T0 #Hn #X1 #H1 #X2 #H2 #L1 #HL01 #L2 #HL02 destruct
+| #I #V0 #T0 #HL #HT #X1 #H1 #X2 #H2 #L1 #HL01 #L2 #HL02 destruct
   elim (cpr_inv_flat1 … H1) -H1 *
   [ #V1 #T1 #HV01 #HT01 #H1
   | #HX1 #H1
-  | #a1 #V1 #Y1 #Z1 #T1 #HV01 #HZT1 #H11 #H12 #H13
+  | #a1 #V1 #Y1 #W1 #Z1 #T1 #HV01 #HYW1 #HZT1 #H11 #H12 #H13
   | #a1 #V1 #U1 #Y1 #W1 #Z1 #T1 #HV01 #HVU1 #HYW1 #HZT1 #H11 #H12 #H13
   ]
   elim (cpr_inv_flat1 … H2) -H2 *
   [1,5,9,13: #V2 #T2 #HV02 #HT02 #H2
   |2,6,10,14: #HX2 #H2
-  |3,7,11,15: #a2 #V2 #Y2 #Z2 #T2 #HV02 #HZT2 #H21 #H22 #H23
+  |3,7,11,15: #a2 #V2 #Y2 #W2 #Z2 #T2 #HV02 #HYW2 #HZT2 #H21 #H22 #H23
   |4,8,12,16: #a2 #V2 #U2 #Y2 #W2 #Z2 #T2 #HV02 #HVU2 #HYW2 #HZT2 #H21 #H22 #H23
   ] destruct
   [ /3 width=10 by cpr_conf_lpr_flat_flat/
   | /4 width=8 by ex2_commute, cpr_conf_lpr_flat_tau/
-  | /4 width=11 by ex2_commute, cpr_conf_lpr_flat_beta/
+  | /4 width=12 by ex2_commute, cpr_conf_lpr_flat_beta/
   | /4 width=14 by ex2_commute, cpr_conf_lpr_flat_theta/
   | /3 width=8 by cpr_conf_lpr_flat_tau/
   | /3 width=7 by cpr_conf_lpr_tau_tau/
-  | /3 width=11 by cpr_conf_lpr_flat_beta/
-  | /3 width=11 by cpr_conf_lpr_beta_beta/
+  | /3 width=12 by cpr_conf_lpr_flat_beta/
+  | /3 width=13 by cpr_conf_lpr_beta_beta/
   | /3 width=14 by cpr_conf_lpr_flat_theta/
   | /3 width=17 by cpr_conf_lpr_theta_theta/
   ]