update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_lpxs.ma
index 9598d49d0c41c47d62dcaed5dab34005edcb25dc..f0a53e660691063120d6c34f2e8e67a7dc496a60 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_lpxs.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/lpxs_rdeq.ma".
+include "basic_2/rt_computation/lpxs_reqx.ma".
 include "basic_2/rt_computation/lpxs_lpxs.ma".
 include "basic_2/rt_computation/rsx_rsx.ma".
 
@@ -22,71 +22,71 @@ include "basic_2/rt_computation/rsx_rsx.ma".
 
 (* Basic_2A1: uses: lsx_intro_alt *)
 lemma rsx_intro_lpxs (h) (G):
-      â\88\80L1,T. (â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88*[h] L2 â\86\92 (L1 â\89\9b[T] L2 â\86\92 â\8a¥) â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L2â¦\84) →
-      G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84.
+      â\88\80L1,T. (â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â¬\88*[h] L2 â\86\92 (L1 â\89\9b[T] L2 â\86\92 â\8a¥) â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL2â\9d«) →
+      G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d«.
 /4 width=1 by lpx_lpxs, rsx_intro/ qed-.
 
 (* Basic_2A1: uses: lsx_lpxs_trans *)
 lemma rsx_lpxs_trans (h) (G):
-      â\88\80L1,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84 →
-      â\88\80L2. â¦\83G,L1â¦\84 â\8a¢ â¬\88*[h] L2 â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L2â¦\84.
+      â\88\80L1,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d« →
+      â\88\80L2. â\9dªG,L1â\9d« â\8a¢ â¬\88*[h] L2 â\86\92 G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL2â\9d«.
 #h #G #L1 #T #HL1 #L2 #H @(lpxs_ind_dx … H) -L2
 /2 width=3 by rsx_lpx_trans/
 qed-.
 
 (* Eliminators with unbound rt-computation for full local environments ******)
 
-lemma rsx_ind_lpxs_rdeq (h) (G) (T) (Q:predicate lenv):
-      (â\88\80L1. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84 →
-            (â\88\80L2. â¦\83G,L1â¦\84 ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
+lemma rsx_ind_lpxs_reqx (h) (G) (T) (Q:predicate lenv):
+      (â\88\80L1. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d« →
+            (â\88\80L2. â\9dªG,L1â\9d« ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
             Q L1
       ) →
-      â\88\80L1. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84  →
-      â\88\80L0. â¦\83G,L1â¦\84 ⊢ ⬈*[h] L0 → ∀L2. L0 ≛[T] L2 → Q L2.
+      â\88\80L1. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d«  →
+      â\88\80L0. â\9dªG,L1â\9d« ⊢ ⬈*[h] L0 → ∀L2. L0 ≛[T] L2 → Q L2.
 #h #G #T #Q #IH #L1 #H @(rsx_ind … H) -L1
 #L1 #HL1 #IH1 #L0 #HL10 #L2 #HL02
-@IH -IH /3 width=3 by rsx_lpxs_trans, rsx_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 L1 L0 T) #H
-[ lapply (rdeq_rdneq_trans … H … HnLK0) -H -HnLK0 #Hn10
+@IH -IH /3 width=3 by rsx_lpxs_trans, rsx_reqx_trans/ -HL1 #K2 #HLK2 #HnLK2
+lapply (reqx_rneqx_trans … HL02 … HnLK2) -HnLK2 #H
+elim (reqx_lpxs_trans … HLK2 … HL02) -L2 #K0 #HLK0 #HK02
+lapply (rneqx_reqx_canc_dx … H … HK02) -H #HnLK0
+elim (reqx_dec L1 L0 T) #H
+[ lapply (reqx_rneqx_trans … H … HnLK0) -H -HnLK0 #Hn10
   lapply (lpxs_trans … HL10 … HLK0) -L0 #H10
-  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/
+  elim (lpxs_rneqx_inv_step_sn … H10 …  Hn10) -H10 -Hn10
+  /3 width=8 by reqx_trans/
+| elim (lpxs_rneqx_inv_step_sn … HL10 … H) -HL10 -H #L #K #HL1 #HnL1 #HLK #HKL0
+  elim (reqx_lpxs_trans … HLK0 … HKL0) -L0
+  /3 width=8 by lpxs_trans, reqx_trans/
 ]
 qed-.
 
 (* Basic_2A1: uses: lsx_ind_alt *)
 lemma rsx_ind_lpxs (h) (G) (T) (Q:predicate lenv):
-      (â\88\80L1. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L1â¦\84 →
-            (â\88\80L2. â¦\83G,L1â¦\84 ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
+      (â\88\80L1. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL1â\9d« →
+            (â\88\80L2. â\9dªG,L1â\9d« ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) → Q L2) →
             Q L1
       ) →
-      â\88\80L. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83Lâ¦\84  → Q L.
+      â\88\80L. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªLâ\9d«  → Q L.
 #h #G #T #Q #IH #L #HL
-@(rsx_ind_lpxs_rdeq … IH … HL) -IH -HL // (**) (* full auto fails *)
+@(rsx_ind_lpxs_reqx … IH … HL) -IH -HL // (**) (* full auto fails *)
 qed-.
 
 (* Advanced properties ******************************************************)
 
 fact rsx_bind_lpxs_aux (h) (G):
-     â\88\80p,I,L1,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83L1â¦\84 →
-     â\88\80Y,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83Yâ¦\84 →
-     ∀L2. Y = L2.ⓑ{I}V → ⦃G,L1⦄ ⊢ ⬈*[h] L2 →
-     G ⊢ ⬈*[h,ⓑ{p,I}V.T] 𝐒⦃L2⦄.
+     â\88\80p,I,L1,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªL1â\9d« →
+     â\88\80Y,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªYâ\9d« →
+     ∀L2. Y = L2.ⓑ[I]V → ❪G,L1❫ ⊢ ⬈*[h] L2 →
+     G ⊢ ⬈*[h,ⓑ[p,I]V.T] 𝐒❪L2❫.
 #h #G #p #I #L1 #V #H @(rsx_ind_lpxs … H) -L1
 #L1 #_ #IHL1 #Y #T #H @(rsx_ind_lpxs … H) -Y
 #Y #HY #IHY #L2 #H #HL12 destruct
 @rsx_intro_lpxs #L0 #HL20
 lapply (lpxs_trans … HL12 … HL20) #HL10 #H
-elim (rdneq_inv_bind … H) -H [ -IHY | -HY -IHL1 -HL12 ]
-[ #HnV elim (rdeq_dec L1 L2 V)
+elim (rneqx_inv_bind … H) -H [ -IHY | -HY -IHL1 -HL12 ]
+[ #HnV elim (reqx_dec L1 L2 V)
   [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10
-    /3 width=4 by rsx_lpxs_trans, lpxs_bind_refl_dx, rdeq_canc_sn/ (**) (* full auto too slow *)
+    /3 width=4 by rsx_lpxs_trans, lpxs_bind_refl_dx, reqx_canc_sn/ (**) (* full auto too slow *)
   | -HnV -HL10 /4 width=4 by rsx_lpxs_trans, lpxs_bind_refl_dx/
   ]
 | /3 width=4 by lpxs_bind_refl_dx/
@@ -95,24 +95,24 @@ qed-.
 
 (* Basic_2A1: uses: lsx_bind *)
 lemma rsx_bind (h) (G):
-      â\88\80p,I,L,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83Lâ¦\84 →
-      â\88\80T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L.â\93\91{I}Vâ¦\84 →
-      G ⊢ ⬈*[h,ⓑ{p,I}V.T] 𝐒⦃L⦄.
+      â\88\80p,I,L,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªLâ\9d« →
+      â\88\80T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL.â\93\91[I]Vâ\9d« →
+      G ⊢ ⬈*[h,ⓑ[p,I]V.T] 𝐒❪L❫.
 /2 width=3 by rsx_bind_lpxs_aux/ qed.
 
 (* Basic_2A1: uses: lsx_flat_lpxs *)
 lemma rsx_flat_lpxs (h) (G):
-      â\88\80I,L1,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83L1â¦\84 →
-      â\88\80L2,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L2â¦\84 â\86\92 â¦\83G,L1â¦\84 ⊢ ⬈*[h] L2 →
-      G ⊢ ⬈*[h,ⓕ{I}V.T] 𝐒⦃L2⦄.
+      â\88\80I,L1,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªL1â\9d« →
+      â\88\80L2,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL2â\9d« â\86\92 â\9dªG,L1â\9d« ⊢ ⬈*[h] L2 →
+      G ⊢ ⬈*[h,ⓕ[I]V.T] 𝐒❪L2❫.
 #h #G #I #L1 #V #H @(rsx_ind_lpxs … H) -L1
 #L1 #HL1 #IHL1 #L2 #T #H @(rsx_ind_lpxs … H) -L2
 #L2 #HL2 #IHL2 #HL12 @rsx_intro_lpxs
 #L0 #HL20 lapply (lpxs_trans … HL12 … HL20)
-#HL10 #H elim (rdneq_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
-[ #HnV elim (rdeq_dec L1 L2 V)
+#HL10 #H elim (rneqx_inv_flat … H) -H [ -HL1 -IHL2 | -HL2 -IHL1 ]
+[ #HnV elim (reqx_dec L1 L2 V)
   [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10
-    /3 width=5 by rsx_lpxs_trans, rdeq_canc_sn/ (**) (* full auto too slow: 47s *)
+    /3 width=5 by rsx_lpxs_trans, reqx_canc_sn/ (**) (* full auto too slow: 47s *)
   | -HnV -HL10 /3 width=4 by rsx_lpxs_trans/
   ]
 | /3 width=3 by/
@@ -121,24 +121,24 @@ qed-.
 
 (* Basic_2A1: uses: lsx_flat *)
 lemma rsx_flat (h) (G):
-      â\88\80I,L,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83Lâ¦\84 →
-      â\88\80T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83Lâ¦\84 â\86\92 G â\8a¢ â¬\88*[h,â\93\95{I}V.T] ð\9d\90\92â¦\83Lâ¦\84.
+      â\88\80I,L,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªLâ\9d« →
+      â\88\80T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªLâ\9d« â\86\92 G â\8a¢ â¬\88*[h,â\93\95[I]V.T] ð\9d\90\92â\9dªLâ\9d«.
 /2 width=3 by rsx_flat_lpxs/ qed.
 
 fact rsx_bind_lpxs_void_aux (h) (G):
-     â\88\80p,I,L1,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83L1â¦\84 →
-     â\88\80Y,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83Yâ¦\84 →
-     â\88\80L2. Y = L2.â\93§ â\86\92 â¦\83G,L1â¦\84 ⊢ ⬈*[h] L2 →
-     G ⊢ ⬈*[h,ⓑ{p,I}V.T] 𝐒⦃L2⦄.
+     â\88\80p,I,L1,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªL1â\9d« →
+     â\88\80Y,T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªYâ\9d« →
+     â\88\80L2. Y = L2.â\93§ â\86\92 â\9dªG,L1â\9d« ⊢ ⬈*[h] L2 →
+     G ⊢ ⬈*[h,ⓑ[p,I]V.T] 𝐒❪L2❫.
 #h #G #p #I #L1 #V #H @(rsx_ind_lpxs … H) -L1
 #L1 #_ #IHL1 #Y #T #H @(rsx_ind_lpxs … H) -Y
 #Y #HY #IHY #L2 #H #HL12 destruct
 @rsx_intro_lpxs #L0 #HL20
 lapply (lpxs_trans … HL12 … HL20) #HL10 #H
-elim (rdneq_inv_bind_void … H) -H [ -IHY | -HY -IHL1 -HL12 ]
-[ #HnV elim (rdeq_dec L1 L2 V)
+elim (rneqx_inv_bind_void … H) -H [ -IHY | -HY -IHL1 -HL12 ]
+[ #HnV elim (reqx_dec L1 L2 V)
   [ #HV @(IHL1 … HL10) -IHL1 -HL12 -HL10
-    /3 width=6 by rsx_lpxs_trans, lpxs_bind_refl_dx, rdeq_canc_sn/ (**) (* full auto too slow *)
+    /3 width=6 by rsx_lpxs_trans, lpxs_bind_refl_dx, reqx_canc_sn/ (**) (* full auto too slow *)
   | -HnV -HL10 /4 width=4 by rsx_lpxs_trans, lpxs_bind_refl_dx/
   ]
 | /3 width=4 by lpxs_bind_refl_dx/
@@ -146,7 +146,7 @@ elim (rdneq_inv_bind_void … H) -H [ -IHY | -HY -IHL1 -HL12 ]
 qed-.
 
 lemma rsx_bind_void (h) (G):
-      â\88\80p,I,L,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â¦\83Lâ¦\84 →
-      â\88\80T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â¦\83L.â\93§â¦\84 →
-      G ⊢ ⬈*[h,ⓑ{p,I}V.T] 𝐒⦃L⦄.
+      â\88\80p,I,L,V. G â\8a¢ â¬\88*[h,V] ð\9d\90\92â\9dªLâ\9d« →
+      â\88\80T. G â\8a¢ â¬\88*[h,T] ð\9d\90\92â\9dªL.â\93§â\9d« →
+      G ⊢ ⬈*[h,ⓑ[p,I]V.T] 𝐒❪L❫.
 /2 width=3 by rsx_bind_lpxs_void_aux/ qed.