- name changes in the rediction rules

[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 933bcd6377f91b2e98ca2da43d869db32c2fe725..ebf3d640637289cc28484eb0cb9470dc0004e74c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_lpr.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/grammar/lpx_sn_lpx_sn.ma".
+include "basic_2/relocation/lpx_sn_lpx_sn.ma".
 include "basic_2/substitution/fqup.ma".
 include "basic_2/reduction/lpr_ldrop.ma".
 
@@ -26,12 +26,12 @@ fact cpr_conf_lpr_atom_atom:
 
 fact cpr_conf_lpr_atom_delta:
    ∀G,L0,i. (
-      â\88\80L,T. â¦\83G, L0, #iâ¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, #iâ¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
    ) →
-   ∀K0,V0. ⇩[O, i] L0 ≡ K0.ⓓV0 →
+   ∀K0,V0. ⇩[i] L0 ≡ K0.ⓓV0 →
    ∀V2. ⦃G, K0⦄ ⊢ V0 ➡ V2 → ∀T2. ⇧[O, i + 1] V2 ≡ T2 →
    ∀L1. ⦃G, L0⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡ L2 →
    ∃∃T. ⦃G, L1⦄ ⊢ #i ➡ T & ⦃G, L2⦄ ⊢ T2 ➡ T.
@@ -40,24 +40,24 @@ elim (lpr_ldrop_conf … HLK0 … HL01) -HL01 #X1 #H1 #HLK1
 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_fwd_drop2 … HLK2) -W2 #HLK2
 lapply (fqup_lref … G … HLK0) -HLK0 #HLK0
 elim (IH … HLK0 … HV01 … HV02 … HK01 … HK02) -L0 -K0 -V0 #V #HV1 #HV2
 elim (lift_total V 0 (i+1))
-/3 width=11 by cpr_lift, cpr_delta, ex2_intro/
+/3 width=12 by cpr_lift, cpr_delta, ex2_intro/
 qed-.
 
 (* Basic_1: includes: pr0_delta_delta pr2_delta_delta *)
 fact cpr_conf_lpr_delta_delta:
    ∀G,L0,i. (
-      â\88\80L,T. â¦\83G, L0, #iâ¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, #iâ¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
    ) →
-   ∀K0,V0. ⇩[O, i] L0 ≡ K0.ⓓV0 →
+   ∀K0,V0. ⇩[i] L0 ≡ K0.ⓓV0 →
    ∀V1. ⦃G, K0⦄ ⊢ V0 ➡ V1 → ∀T1. ⇧[O, i + 1] V1 ≡ T1 →
-   ∀KX,VX. ⇩[O, i] L0 ≡ KX.ⓓVX →
+   ∀KX,VX. ⇩[i] L0 ≡ KX.ⓓVX →
    ∀V2. ⦃G, KX⦄ ⊢ VX ➡ V2 → ∀T2. ⇧[O, i + 1] V2 ≡ T2 →
    ∀L1. ⦃G, L0⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡ L2 →
    ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡ T & ⦃G, L2⦄ ⊢ T2 ➡ T.
@@ -66,18 +66,18 @@ fact cpr_conf_lpr_delta_delta:
 lapply (ldrop_mono … H … HLK0) -H #H destruct
 elim (lpr_ldrop_conf … HLK0 … HL01) -HL01 #X1 #H1 #HLK1
 elim (lpr_inv_pair1 … H1) -H1 #K1 #W1 #HK01 #_ #H destruct
-lapply (ldrop_fwd_ldrop2 … HLK1) -W1 #HLK1
+lapply (ldrop_fwd_drop2 … 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_fwd_drop2 … HLK2) -W2 #HLK2
 lapply (fqup_lref … G … HLK0) -HLK0 #HLK0
 elim (IH … HLK0 … HV01 … HV02 … HK01 … HK02) -L0 -K0 -V0 #V #HV1 #HV2
-elim (lift_total V 0 (i+1)) /3 width=11 by cpr_lift, ex2_intro/
+elim (lift_total V 0 (i+1)) /3 width=12 by cpr_lift, ex2_intro/
 qed-.
 
 fact cpr_conf_lpr_bind_bind:
    ∀a,I,G,L0,V0,T0. (
-      â\88\80L,T. â¦\83G, L0, â\93\91{a,I}V0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, â\93\91{a,I}V0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -95,7 +95,7 @@ qed-.
 
 fact cpr_conf_lpr_bind_zeta:
    ∀G,L0,V0,T0. (
-      â\88\80L,T. â¦\83G, L0, +â\93\93V0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, +â\93\93V0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -107,12 +107,12 @@ fact cpr_conf_lpr_bind_zeta:
 #G #L0 #V0 #T0 #IH #V1 #HV01 #T1 #HT01
 #T2 #HT02 #X2 #HXT2 #L1 #HL01 #L2 #HL02
 elim (IH … HT01 … HT02 (L1.ⓓV1) … (L2.ⓓV1)) -IH -HT01 -HT02 /2 width=1 by lpr_pair/ -L0 -V0 -T0 #T #HT1 #HT2
-elim (cpr_inv_lift1 … HT2 L2 … HXT2) -T2 /3 width=3 by cpr_zeta, ldrop_ldrop, ex2_intro/
+elim (cpr_inv_lift1 … HT2 L2 … HXT2) -T2 /3 width=3 by cpr_zeta, ldrop_drop, ex2_intro/
 qed-.
 
 fact cpr_conf_lpr_zeta_zeta:
    ∀G,L0,V0,T0. (
-      â\88\80L,T. â¦\83G, L0, +â\93\93V0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, +â\93\93V0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -124,14 +124,14 @@ fact cpr_conf_lpr_zeta_zeta:
 #G #L0 #V0 #T0 #IH #T1 #HT01 #X1 #HXT1
 #T2 #HT02 #X2 #HXT2 #L1 #HL01 #L2 #HL02
 elim (IH … HT01 … HT02 (L1.ⓓV0) … (L2.ⓓV0)) -IH -HT01 -HT02 /2 width=1 by lpr_pair/ -L0 -T0 #T #HT1 #HT2
-elim (cpr_inv_lift1 … HT1 L1 … HXT1) -T1 /2 width=1 by ldrop_ldrop/ #T1 #HT1 #HXT1
-elim (cpr_inv_lift1 … HT2 L2 … HXT2) -T2 /2 width=1 by ldrop_ldrop/ #T2 #HT2 #HXT2
+elim (cpr_inv_lift1 … HT1 L1 … HXT1) -T1 /2 width=2 by ldrop_drop/ #T1 #HT1 #HXT1
+elim (cpr_inv_lift1 … HT2 L2 … HXT2) -T2 /2 width=2 by ldrop_drop/ #T2 #HT2 #HXT2
 lapply (lift_inj … HT2 … HT1) -T #H destruct /2 width=3 by ex2_intro/
 qed-.
 
 fact cpr_conf_lpr_flat_flat:
    ∀I,G,L0,V0,T0. (
-      â\88\80L,T. â¦\83G, L0, â\93\95{I}V0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, â\93\95{I}V0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -146,9 +146,9 @@ elim (IH … HV01 … HV02 … HL01 … HL02) //
 elim (IH … HT01 … HT02 … HL01 … HL02) /3 width=5 by cpr_flat, ex2_intro/
 qed-.
 
-fact cpr_conf_lpr_flat_tau:
+fact cpr_conf_lpr_flat_eps:
    ∀G,L0,V0,T0. (
-      â\88\80L,T. â¦\83G, L0, â\93\9dV0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, â\93\9dV0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -158,12 +158,12 @@ fact cpr_conf_lpr_flat_tau:
    ∃∃T. ⦃G, L1⦄ ⊢ ⓝV1.T1 ➡ T & ⦃G, L2⦄ ⊢ T2 ➡ T.
 #G #L0 #V0 #T0 #IH #V1 #T1 #HT01
 #T2 #HT02 #L1 #HL01 #L2 #HL02
-elim (IH … HT01 … HT02 … HL01 … HL02) // -L0 -V0 -T0 /3 width=3 by cpr_tau, ex2_intro/
+elim (IH … HT01 … HT02 … HL01 … HL02) // -L0 -V0 -T0 /3 width=3 by cpr_eps, ex2_intro/
 qed-.
 
-fact cpr_conf_lpr_tau_tau:
+fact cpr_conf_lpr_eps_eps:
    ∀G,L0,V0,T0. (
-      â\88\80L,T. â¦\83G, L0, â\93\9dV0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, â\93\9dV0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -178,7 +178,7 @@ qed-.
 
 fact cpr_conf_lpr_flat_beta:
    ∀a,G,L0,V0,W0,T0. (
-      â\88\80L,T. â¦\83G, L0, â\93\90V0.â\93\9b{a}W0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, â\93\90V0.â\93\9b{a}W0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -203,7 +203,7 @@ qed-.
 *)
 fact cpr_conf_lpr_flat_theta:
    ∀a,G,L0,V0,W0,T0. (
-      â\88\80L,T. â¦\83G, L0, â\93\90V0.â\93\93{a}W0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, â\93\90V0.â\93\93{a}W0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -217,7 +217,7 @@ fact cpr_conf_lpr_flat_theta:
 #V2 #HV02 #U2 #HVU2 #W2 #HW02 #T2 #HT02 #L1 #HL01 #L2 #HL02
 elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1 by/ #V #HV1 #HV2
 elim (lift_total V 0 1) #U #HVU
-lapply (cpr_lift … HV2 (L2.ⓓW2) … HVU2 … HVU) -HVU2 /2 width=1 by ldrop_ldrop/ #HU2
+lapply (cpr_lift … HV2 (L2.ⓓW2) … HVU2 … HVU) -HVU2 /2 width=2 by ldrop_drop/ #HU2
 elim (cpr_inv_abbr1 … H) -H *
 [ #W1 #T1 #HW01 #HT01 #H destruct
   elim (IH … HW01 … HW02 … HL01 … HL02) /2 width=1 by/
@@ -226,13 +226,13 @@ elim (cpr_inv_abbr1 … H) -H *
 | #T1 #HT01 #HXT1 #H destruct
   elim (IH … HT01 … HT02 (L1.ⓓW2) … (L2.ⓓW2)) /2 width=1 by lpr_pair/ -L0 -V0 -W0 -T0 #T #HT1 #HT2
   elim (cpr_inv_lift1 … HT1 L1 … HXT1) -HXT1
-  /4 width=9 by cpr_flat, cpr_zeta, ldrop_ldrop, lift_flat, ex2_intro/
+  /4 width=9 by cpr_flat, cpr_zeta, ldrop_drop, lift_flat, ex2_intro/
 ]
 qed-.
 
 fact cpr_conf_lpr_beta_beta:
    ∀a,G,L0,V0,W0,T0. (
-      â\88\80L,T. â¦\83G, L0, â\93\90V0.â\93\9b{a}W0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, â\93\90V0.â\93\9b{a}W0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -254,7 +254,7 @@ qed-.
 (* Basic_1: was: pr0_upsilon_upsilon *)
 fact cpr_conf_lpr_theta_theta:
    ∀a,G,L0,V0,W0,T0. (
-      â\88\80L,T. â¦\83G, L0, â\93\90V0.â\93\93{a}W0.T0â¦\84 â\8a\83+ ⦃G, L, T⦄ →
+      â\88\80L,T. â¦\83G, L0, â\93\90V0.â\93\93{a}W0.T0â¦\84 â\8a\90+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
       ∀L1. ⦃G, L⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L⦄ ⊢ ➡ L2 →
       ∃∃T0. ⦃G, L1⦄ ⊢ T1 ➡ T0 & ⦃G, L2⦄ ⊢ T2 ➡ T0
@@ -271,8 +271,8 @@ elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1 by/ #V #HV1
 elim (IH … HW01 … HW02 … HL01 … HL02) /2 width=1 by/
 elim (IH … HT01 … HT02 (L1.ⓓW1) … (L2.ⓓW2)) /2 width=1 by lpr_pair/ -L0 -V0 -W0 -T0
 elim (lift_total V 0 1) #U #HVU
-lapply (cpr_lift … HV1 (L1.ⓓW1) … HVU1 … HVU) -HVU1 /2 width=1 by ldrop_ldrop/
-lapply (cpr_lift … HV2 (L2.ⓓW2) … HVU2 … HVU) -HVU2 /2 width=1 by ldrop_ldrop/
+lapply (cpr_lift … HV1 (L1.ⓓW1) … HVU1 … HVU) -HVU1 /2 width=2 by ldrop_drop/
+lapply (cpr_lift … HV2 (L2.ⓓW2) … HVU2 … HVU) -HVU2 /2 width=2 by ldrop_drop/
 /4 width=7 by cpr_bind, cpr_flat, ex2_intro/ (**) (* full auto not tried *)
 qed-.
 
@@ -319,11 +319,11 @@ theorem cpr_conf_lpr: ∀G. lpx_sn_confluent (cpr G) (cpr G).
   |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=8 by ex2_commute, cpr_conf_lpr_flat_eps/
   | /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=8 by cpr_conf_lpr_flat_eps/
+  | /3 width=7 by cpr_conf_lpr_eps_eps/
   | /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/
@@ -341,13 +341,13 @@ theorem cpr_conf: ∀G,L. confluent … (cpr G L).
 lemma lpr_cpr_conf_dx: ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡ T1 → ∀L1. ⦃G, L0⦄ ⊢ ➡ L1 →
                        ∃∃T. ⦃G, L1⦄ ⊢ T0 ➡ T & ⦃G, L1⦄ ⊢ T1 ➡ T.
 #G #L0 #T0 #T1 #HT01 #L1 #HL01
-elim (cpr_conf_lpr … HT01 T0 … HL01 … HL01) // -L0 /2 width=3 by ex2_intro/
+elim (cpr_conf_lpr … HT01 T0 … HL01 … HL01) /2 width=3 by ex2_intro/
 qed-.
 
 lemma lpr_cpr_conf_sn: ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡ T1 → ∀L1. ⦃G, L0⦄ ⊢ ➡ L1 →
                        ∃∃T. ⦃G, L1⦄ ⊢ T0 ➡ T & ⦃G, L0⦄ ⊢ T1 ➡ T.
 #G #L0 #T0 #T1 #HT01 #L1 #HL01
-elim (cpr_conf_lpr … HT01 T0 … L0 … HL01) // -HT01 -HL01 /2 width=3 by ex2_intro/
+elim (cpr_conf_lpr … HT01 T0 … L0 … HL01) /2 width=3 by ex2_intro/
 qed-.
 
 (* Main properties **********************************************************)