renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / rdsx_lpxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_lpxs.ma
index c9f49cfe19c41c5eaf0085dd4a3e6707f10b8cd2..06649215c638c3237c828a5e906decd5a2ac7490 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_lpxs.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/lpxs_lfdeq.ma".
+include "basic_2/rt_computation/lpxs_rdeq.ma".
 include "basic_2/rt_computation/lpxs_lpxs.ma".
 include "basic_2/rt_computation/rdsx_rdsx.ma".
 
@@ -35,28 +35,28 @@ qed-.
 
 (* Eliminators with unbound rt-computation for full local environments ******)
 
-lemma rdsx_ind_lpxs_lfdeq (h) (o) (G):
-                          ∀T. ∀Q:predicate lenv.
-                          (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
-                                (∀L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → Q L2) →
-                                Q L1
-                          ) →
-                          ∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄  →
-                          ∀L0. ⦃G, L1⦄ ⊢ ⬈*[h] L0 → ∀L2. L0 ≛[h, o, T] L2 → Q L2.
+lemma rdsx_ind_lpxs_rdeq (h) (o) (G):
+                         ∀T. ∀Q:predicate lenv.
+                         (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
+                               (∀L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → Q L2) →
+                               Q L1
+                         ) →
+                         ∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄  →
+                         ∀L0. ⦃G, L1⦄ ⊢ ⬈*[h] L0 → ∀L2. L0 ≛[h, o, T] L2 → Q L2.
 #h #o #G #T #Q #IH #L1 #H @(rdsx_ind … H) -L1
 #L1 #HL1 #IH1 #L0 #HL10 #L2 #HL02
-@IH -IH /3 width=3 by rdsx_lpxs_trans, rdsx_lfdeq_trans/ -HL1 #K2 #HLK2 #HnLK2
-lapply (lfdeq_lfdneq_trans … HL02 … HnLK2) -HnLK2 #H
-elim (lfdeq_lpxs_trans … HLK2 … HL02) -L2 #K0 #HLK0 #HK02
-lapply (lfdneq_lfdeq_canc_dx … H … HK02) -H #HnLK0
-elim (lfdeq_dec h o L1 L0 T) #H
-[ lapply (lfdeq_lfdneq_trans … H … HnLK0) -H -HnLK0 #Hn10
+@IH -IH /3 width=3 by rdsx_lpxs_trans, rdsx_rdeq_trans/ -HL1 #K2 #HLK2 #HnLK2
+lapply (rdeq_rdneq_trans … HL02 … HnLK2) -HnLK2 #H
+elim (rdeq_lpxs_trans … HLK2 … HL02) -L2 #K0 #HLK0 #HK02
+lapply (rdneq_rdeq_canc_dx … H … HK02) -H #HnLK0
+elim (rdeq_dec h o L1 L0 T) #H
+[ lapply (rdeq_rdneq_trans … H … HnLK0) -H -HnLK0 #Hn10
   lapply (lpxs_trans … HL10 … HLK0) -L0 #H10
-  elim (lpxs_lfdneq_inv_step_sn … H10 …  Hn10) -H10 -Hn10
-  /3 width=8 by lfdeq_trans/
-| elim (lpxs_lfdneq_inv_step_sn … HL10 … H) -HL10 -H #L #K #HL1 #HnL1 #HLK #HKL0
-  elim (lfdeq_lpxs_trans … HLK0 … HKL0) -L0
-  /3 width=8 by lpxs_trans, lfdeq_trans/
+  elim (lpxs_rdneq_inv_step_sn … H10 …  Hn10) -H10 -Hn10
+  /3 width=8 by rdeq_trans/
+| elim (lpxs_rdneq_inv_step_sn … HL10 … H) -HL10 -H #L #K #HL1 #HnL1 #HLK #HKL0
+  elim (rdeq_lpxs_trans … HLK0 … HKL0) -L0
+  /3 width=8 by lpxs_trans, rdeq_trans/
 ]
 qed-.
 
@@ -69,7 +69,7 @@ lemma rdsx_ind_lpxs (h) (o) (G):
                     ) →
                     ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄  → Q L.
 #h #o #G #T #Q #IH #L #HL
-@(rdsx_ind_lpxs_lfdeq … IH … HL) -IH -HL // (**) (* full auto fails *)
+@(rdsx_ind_lpxs_rdeq … IH … HL) -IH -HL // (**) (* full auto fails *)
 qed-.
 
 (* Advanced properties ******************************************************)
@@ -84,10 +84,10 @@ fact rdsx_bind_lpxs_aux (h) (o) (G):
 #Y #HY #IHY #L2 #H #HL12 destruct
 @rdsx_intro_lpxs #L0 #HL20
 lapply (lpxs_trans … HL12 … HL20) #HL10 #H
-elim (lfdneq_inv_bind … H) -H [ -IHY | -HY -IHL1 -HL12 ]
-[ #HnV elim (lfdeq_dec h o L1 L2 V)
+elim (rdneq_inv_bind … H) -H [ -IHY | -HY -IHL1 -HL12 ]
+[ #HnV elim (rdeq_dec h o L1 L2 V)
   [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10
-    /3 width=4 by rdsx_lpxs_trans, lpxs_bind_refl_dx, lfdeq_canc_sn/ (**) (* full auto too slow *)
+    /3 width=4 by rdsx_lpxs_trans, lpxs_bind_refl_dx, rdeq_canc_sn/ (**) (* full auto too slow *)
   | -HnV -HL10 /4 width=4 by rdsx_lpxs_trans, lpxs_bind_refl_dx/
   ]
 | /3 width=4 by lpxs_bind_refl_dx/
@@ -110,10 +110,10 @@ lemma rdsx_flat_lpxs (h) (o) (G):
 #L1 #HL1 #IHL1 #L2 #T #H @(rdsx_ind_lpxs … H) -L2
 #L2 #HL2 #IHL2 #HL12 @rdsx_intro_lpxs
 #L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
-#HL10 #H elim (lfdneq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
-[ #HnV elim (lfdeq_dec h o L1 L2 V)
+#HL10 #H elim (rdneq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
+[ #HnV elim (rdeq_dec h o L1 L2 V)
   [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10
-    /3 width=5 by rdsx_lpxs_trans, lfdeq_canc_sn/ (**) (* full auto too slow: 47s *)
+    /3 width=5 by rdsx_lpxs_trans, rdeq_canc_sn/ (**) (* full auto too slow: 47s *)
   | -HnV -HL10 /3 width=4 by rdsx_lpxs_trans/
   ]
 | /3 width=3 by/
@@ -136,10 +136,10 @@ fact rdsx_bind_lpxs_void_aux (h) (o) (G):
 #Y #HY #IHY #L2 #H #HL12 destruct
 @rdsx_intro_lpxs #L0 #HL20
 lapply (lpxs_trans … HL12 … HL20) #HL10 #H
-elim (lfdneq_inv_bind_void … H) -H [ -IHY | -HY -IHL1 -HL12 ]
-[ #HnV elim (lfdeq_dec h o L1 L2 V)
+elim (rdneq_inv_bind_void … H) -H [ -IHY | -HY -IHL1 -HL12 ]
+[ #HnV elim (rdeq_dec h o L1 L2 V)
   [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10
-    /3 width=6 by rdsx_lpxs_trans, lpxs_bind_refl_dx, lfdeq_canc_sn/ (**) (* full auto too slow *)
+    /3 width=6 by rdsx_lpxs_trans, lpxs_bind_refl_dx, rdeq_canc_sn/ (**) (* full auto too slow *)
   | -HnV -HL10 /4 width=4 by rdsx_lpxs_trans, lpxs_bind_refl_dx/
   ]
 | /3 width=4 by lpxs_bind_refl_dx/