update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
index 98bed39de105e13dd752c4e238326093503e849f..e3ad463a62b98704bfd70ee1e04a6ea1cfa3006c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
@@ -12,6 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/rt_transition/fpbc_fqup.ma".
+include "basic_2/rt_transition/fpbc_lpx.ma".
 include "basic_2/rt_computation/rsx_csx.ma".
 include "basic_2/rt_computation/fpbs_cpx.ma".
 include "basic_2/rt_computation/fpbs_csx.ma".
@@ -21,58 +23,66 @@ include "basic_2/rt_computation/fsb_fpbg.ma".
 
 (* Inversion lemmas with context-sensitive stringly rt-normalizing terms ****)
 
-lemma fsb_inv_csx: ∀h,G,L,T. ≥[h] 𝐒⦃G,L,T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
-#h #G #L #T #H @(fsb_ind_alt … H) -G -L -T /5 width=1 by csx_intro, fpb_cpx/
+lemma fsb_inv_csx:
+      ∀G,L,T. ≥𝐒 ❪G,L,T❫ → ❪G,L❫ ⊢ ⬈*𝐒 T.
+#G #L #T #H @(fsb_ind … H) -G -L -T
+/5 width=1 by csx_intro, cpx_fpbc/
 qed-.
 
 (* Propreties with context-sensitive stringly rt-normalizing terms **********)
 
-lemma csx_fsb_fpbs: ∀h,G1,L1,T1. ⦃G1,L1⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
-                    ∀G2,L2,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ → ≥[h] 𝐒⦃G2,L2,T2⦄.
-#h #G1 #L1 #T1 #H @(csx_ind … H) -T1
+lemma csx_fsb_fpbs:
+      ∀G1,L1,T1. ❪G1,L1❫ ⊢ ⬈*𝐒 T1 →
+      ∀G2,L2,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫.
+#G1 #L1 #T1 #H @(csx_ind … H) -T1
 #T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind (Ⓣ) … G2 L2 T2) -G2 -L2 -T2
 #G0 #L0 #T0 #IHu #H10
 lapply (fpbs_csx_conf … H10) // -HT1 #HT0
 generalize in match IHu; -IHu generalize in match H10; -H10
-@(rsx_ind … (csx_rsx … HT0)) -L0
-#L0 #_ #IHd #H10 #IHu @fsb_intro
-#G2 #L2 #T2 * -G2 -L2 -T2 [ -IHd -IHc | -IHu -IHd |  ]
-[ /4 width=5 by fpbs_fqup_trans, fqu_fqup/
-| #T2 #HT02 #HnT02
-  elim (fpbs_cpx_tneqx_trans … H10 … HT02 HnT02) -T0
-  /3 width=4 by/
-| #L2 #HL02 #HnL02 @(IHd … HL02 HnL02) -IHd -HnL02 [ -IHu -IHc | ]
+@(rsx_ind … (csx_rsx … HT0)) -L0 #L0 #_ #IHd #H10 #IHu
+@fsb_intro #G2 #L2 #T2 #H
+elim (fpbc_fwd_lpx … H) -H * [ -IHd -IHc | -IHu -IHd |]
+[ /5 width=5 by fsb_fpb_trans, fpbs_fqup_trans, fqu_fqup/
+| #T3 #HT03 #HnT03 #H32
+  elim (fpbs_cpx_tneqg_trans … H10 … HT03 HnT03) -T0
+  /4 width=5 by fsb_fpb_trans, sfull_dec/
+| #L3 #HL03 #HnL03 #HL32
+  @(fsb_fpb_trans … HL32) -L2
+  @(IHd … HL03 HnL03) -IHd -HnL03 [ -IHu -IHc |]
   [ /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/
-  | #G3 #L3 #T3 #H03 #_
-    elim (lpx_fqup_trans … H03 … HL02) -L2 #L4 #T4 #HT04 #H43 #HL43
-    elim (teqx_dec T0 T4) [ -IHc -HT04 #HT04 | -IHu #HnT04 ]
-    [ elim (teqx_fqup_trans … H43 … HT04) -T4 #L2 #T4 #H04 #HT43 #HL24
-      /4 width=7 by fsb_fpbs_trans, teqx_reqx_lpx_fpbs, fpbs_fqup_trans/
-    | elim (cpxs_tneqx_fwd_step_sn … HT04 HnT04) -HT04 -HnT04 #T2 #T5 #HT02 #HnT02 #HT25 #HT54
-      elim (fpbs_cpx_tneqx_trans … H10 … HT02 HnT02) -T0 #T0 #HT10 #HnT10 #H02
-      /3 width=14 by fpbs_cpxs_teqx_fqup_lpx_trans/
+  | #G4 #L4 #T4 #H04 #_
+    elim (lpx_fqup_trans … H04 … HL03) -L3 #L3 #T3 #HT03 #H34 #HL34
+    elim (teqx_dec T0 T3) [ -IHc -HT03 #HT03 | -IHu #HnT03 ]
+    [ elim (teqg_fqup_trans … H34 … HT03) -T3 // #L2 #T3 #H03 #HT34 #HL23
+      /4 width=10 by fsb_fpbs_trans, teqg_reqg_lpx_fpbs, fpbs_fqup_trans/
+    | elim (cpxs_tneqg_fwd_step_sn … HT03 HnT03) -HT03 -HnT03 /2 width=1 by sfull_dec/ #T2 #HT02 #HnT02 #HT23
+      elim (fpbs_cpx_tneqg_trans … H10 … HT02 HnT02) -T0 /2 width=1 by sfull_dec/ #T0 #HT10 #HnT10 #H02
+      /3 width=17 by fpbs_cpxs_teqg_fqup_lpx_trans/
     ]
   ]
 ]
 qed.
 
-lemma csx_fsb: ∀h,G,L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ≥[h] 𝐒⦃G,L,T⦄.
+lemma csx_fsb (G) (L) (T):
+      ❪G,L❫ ⊢ ⬈*𝐒 T → ≥𝐒 ❪G,L,T❫.
 /2 width=5 by csx_fsb_fpbs/ qed.
 
 (* Advanced eliminators *****************************************************)
 
-lemma csx_ind_fpb: ∀h. ∀Q:relation3 genv lenv term.
-                   (∀G1,L1,T1. ⦃G1,L1⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
-                               (∀G2,L2,T2. ⦃G1,L1,T1⦄ ≻[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
-                               Q G1 L1 T1
-                   ) →
-                   ∀G,L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →  Q G L T.
-/4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
+lemma csx_ind_fpbc (Q:relation3 …):
+      (∀G1,L1,T1.
+        ❪G1,L1❫ ⊢ ⬈*𝐒 T1 →
+        (∀G2,L2,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → Q G2 L2 T2) →
+        Q G1 L1 T1
+      ) →
+      ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → Q G L T.
+/4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind/ qed-.
 
-lemma csx_ind_fpbg: ∀h. ∀Q:relation3 genv lenv term.
-                    (∀G1,L1,T1. ⦃G1,L1⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
-                                (∀G2,L2,T2. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
-                                Q G1 L1 T1
-                    ) →
-                    ∀G,L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →  Q G L T.
+lemma csx_ind_fpbg (Q:relation3 …):
+      (∀G1,L1,T1.
+        ❪G1,L1❫ ⊢ ⬈*𝐒 T1 →
+        (∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → Q G2 L2 T2) →
+        Q G1 L1 T1
+      ) →
+      ∀G,L,T. ❪G,L❫ ⊢ ⬈*𝐒 T → Q G L T.
 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.