- 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 7b65286abff0f3cd83ce10cf0ba844848ca6018b..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".
 
@@ -26,7 +26,7 @@ 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
@@ -50,7 +50,7 @@ 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
@@ -77,7 +77,7 @@ 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
@@ -112,7 +112,7 @@ 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
@@ -131,7 +131,7 @@ 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
@@ -232,7 +232,7 @@ 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
@@ -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/