some renaming and some typos corrected ...

[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 d0b36345539e8b4415e950f93cc84c5108d2b851..2aa2810b13ab29977b562d501bbcb6337e8945b4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/lpr_lpr.ma
@@ -12,9 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/lpx_sn_lpx_sn.ma".
-include "basic_2/substitution/fqup.ma".
-include "basic_2/reduction/lpr_ldrop.ma".
+include "basic_2/substitution/lpx_sn_lpx_sn.ma".
+include "basic_2/multiple/fqup.ma".
+include "basic_2/reduction/lpr_drop.ma".
 
 (* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
 
@@ -36,11 +36,11 @@ fact cpr_conf_lpr_atom_delta:
    ∀L1. ⦃G, L0⦄ ⊢ ➡ L1 → ∀L2. ⦃G, L0⦄ ⊢ ➡ L2 →
    ∃∃T. ⦃G, L1⦄ ⊢ #i ➡ T & ⦃G, L2⦄ ⊢ T2 ➡ T.
 #G #L0 #i #IH #K0 #V0 #HLK0 #V2 #HV02 #T2 #HVT2 #L1 #HL01 #L2 #HL02
-elim (lpr_ldrop_conf … HLK0 … HL01) -HL01 #X1 #H1 #HLK1
+elim (lpr_drop_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_drop_conf … HLK0 … HL02) -HL02 #X2 #H2 #HLK2
 elim (lpr_inv_pair1 … H2) -H2 #K2 #W2 #HK02 #_ #H destruct
-lapply (ldrop_fwd_drop2 … HLK2) -W2 #HLK2
+lapply (drop_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))
@@ -63,13 +63,13 @@ fact cpr_conf_lpr_delta_delta:
    ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡ T & ⦃G, L2⦄ ⊢ T2 ➡ T.
 #G #L0 #i #IH #K0 #V0 #HLK0 #V1 #HV01 #T1 #HVT1
 #KX #VX #H #V2 #HV02 #T2 #HVT2 #L1 #HL01 #L2 #HL02
-lapply (ldrop_mono … H … HLK0) -H #H destruct
-elim (lpr_ldrop_conf … HLK0 … HL01) -HL01 #X1 #H1 #HLK1
+lapply (drop_mono … H … HLK0) -H #H destruct
+elim (lpr_drop_conf … HLK0 … HL01) -HL01 #X1 #H1 #HLK1
 elim (lpr_inv_pair1 … H1) -H1 #K1 #W1 #HK01 #_ #H destruct
-lapply (ldrop_fwd_drop2 … HLK1) -W1 #HLK1
-elim (lpr_ldrop_conf … HLK0 … HL02) -HL02 #X2 #H2 #HLK2
+lapply (drop_fwd_drop2 … HLK1) -W1 #HLK1
+elim (lpr_drop_conf … HLK0 … HL02) -HL02 #X2 #H2 #HLK2
 elim (lpr_inv_pair1 … H2) -H2 #K2 #W2 #HK02 #_ #H destruct
-lapply (ldrop_fwd_drop2 … HLK2) -W2 #HLK2
+lapply (drop_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=12 by cpr_lift, ex2_intro/
@@ -107,7 +107,7 @@ 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_drop, ex2_intro/
+elim (cpr_inv_lift1 … HT2 L2 … HXT2) -T2 /3 width=3 by cpr_zeta, drop_drop, ex2_intro/
 qed-.
 
 fact cpr_conf_lpr_zeta_zeta:
@@ -124,8 +124,8 @@ 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=2 by ldrop_drop/ #T1 #HT1 #HXT1
-elim (cpr_inv_lift1 … HT2 L2 … HXT2) -T2 /2 width=2 by ldrop_drop/ #T2 #HT2 #HXT2
+elim (cpr_inv_lift1 … HT1 L1 … HXT1) -T1 /2 width=2 by drop_drop/ #T1 #HT1 #HXT1
+elim (cpr_inv_lift1 … HT2 L2 … HXT2) -T2 /2 width=2 by drop_drop/ #T2 #HT2 #HXT2
 lapply (lift_inj … HT2 … HT1) -T #H destruct /2 width=3 by ex2_intro/
 qed-.
 
@@ -146,7 +146,7 @@ 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. (
       ∀L,T. ⦃G, L0, ⓝV0.T0⦄ ⊐+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
@@ -158,10 +158,10 @@ 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. (
       ∀L,T. ⦃G, L0, ⓝV0.T0⦄ ⊐+ ⦃G, L, T⦄ →
       ∀T1. ⦃G, L⦄ ⊢ T ➡ T1 → ∀T2. ⦃G, L⦄ ⊢ T ➡ T2 →
@@ -193,7 +193,7 @@ elim (cpr_inv_abst1 … H) -H #W1 #T1 #HW01 #HT01 #H destruct
 elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1 by/ #V #HV1 #HV2
 elim (IH … HW01 … HW02 … HL01 … HL02) /2 width=1 by/ #W #HW1 #HW2
 elim (IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) /2 width=1 by lpr_pair/ -L0 -V0 -W0 -T0 #T #HT1 #HT2
-lapply (lsubr_cpr_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1 by lsubr_abst/ (**) (* full auto not tried *)
+lapply (lsubr_cpr_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1 by lsubr_beta/ (**) (* full auto not tried *)
 /4 width=5 by cpr_bind, cpr_flat, cpr_beta, ex2_intro/
 qed-.
 
@@ -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=2 by ldrop_drop/ #HU2
+lapply (cpr_lift … HV2 (L2.ⓓW2) … HVU2 … HVU) -HVU2 /2 width=2 by drop_drop/ #HU2
 elim (cpr_inv_abbr1 … H) -H *
 [ #W1 #T1 #HW01 #HT01 #H destruct
   elim (IH … HW01 … HW02 … HL01 … HL02) /2 width=1 by/
@@ -226,7 +226,7 @@ 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_drop, lift_flat, ex2_intro/
+  /4 width=9 by cpr_flat, cpr_zeta, drop_drop, lift_flat, ex2_intro/
 ]
 qed-.
 
@@ -246,8 +246,8 @@ fact cpr_conf_lpr_beta_beta:
 elim (IH … HV01 … HV02 … HL01 … HL02) -HV01 -HV02 /2 width=1 by/ #V #HV1 #HV2
 elim (IH … HW01 … HW02 … HL01 … HL02) /2 width=1/ #W #HW1 #HW2
 elim (IH … HT01 … HT02 (L1.ⓛW1) … (L2.ⓛW2)) /2 width=1 by lpr_pair/ -L0 -V0 -W0 -T0 #T #HT1 #HT2
-lapply (lsubr_cpr_trans … HT1 (L1.ⓓⓝW1.V1) ?) -HT1 /2 width=1 by lsubr_abst/
-lapply (lsubr_cpr_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1 by lsubr_abst/
+lapply (lsubr_cpr_trans … HT1 (L1.ⓓⓝW1.V1) ?) -HT1 /2 width=1 by lsubr_beta/
+lapply (lsubr_cpr_trans … HT2 (L2.ⓓⓝW2.V2) ?) -HT2 /2 width=1 by lsubr_beta/
 /4 width=5 by cpr_bind, cpr_flat, ex2_intro/ (**) (* full auto not tried *)
 qed-.
 
@@ -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=2 by ldrop_drop/
-lapply (cpr_lift … HV2 (L2.ⓓW2) … HVU2 … HVU) -HVU2 /2 width=2 by ldrop_drop/
+lapply (cpr_lift … HV1 (L1.ⓓW1) … HVU1 … HVU) -HVU1 /2 width=2 by drop_drop/
+lapply (cpr_lift … HV2 (L2.ⓓW2) … HVU2 … HVU) -HVU2 /2 width=2 by drop_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/