milestone update in basic_2, update in ground and static_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 6d25d649b6a9b19765619a2415bc848085bcb942..1839df0f8a3d800c1237a3c5a005fe2ddefccad8 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
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_computation/lfsx_csx.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".
 include "basic_2/rt_computation/fsb_fpbg.ma".
@@ -21,58 +21,63 @@ include "basic_2/rt_computation/fsb_fpbg.ma".
 
 (* Inversion lemmas with context-sensitive stringly rt-normalizing terms ****)
 
-lemma fsb_inv_csx: ∀h,o,G,L,T. ≥[h, o] 𝐒⦃G, L, T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
-#h #o #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_alt … H) -G -L -T /5 width=1 by csx_intro, fpb_cpx/
 qed-.
 
 (* Propreties with context-sensitive stringly rt-normalizing terms **********)
 
-lemma csx_fsb_fpbs: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                    ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ≥[h, o] 𝐒⦃G2, L2, T2⦄.
-#h #o #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 
+#G0 #L0 #T0 #IHu #H10
 lapply (fpbs_csx_conf … H10) // -HT1 #HT0
 generalize in match IHu; -IHu generalize in match H10; -H10
-@(lfsx_ind … (csx_lfsx … HT0)) -L0
+@(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_tdneq_trans … H10 … HT02 HnT02) -T0
+  elim (fpbs_cpx_tneqx_trans … H10 … HT02 HnT02) -T0
   /3 width=4 by/
 | #L2 #HL02 #HnL02 @(IHd … HL02 HnL02) -IHd -HnL02 [ -IHu -IHc | ]
-  [ /3 width=3 by fpbs_lfpxs_trans, lfpx_lfpxs/
+  [ /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/
   | #G3 #L3 #T3 #H03 #_
-    elim (lfpx_fqup_trans … H03 … HL02) -L2 #L4 #T4 #HT04 #H43 #HL43
-    elim (tdeq_dec h o T0 T4) [ -IHc -HT04 #HT04 | -IHu #HnT04 ]
-    [ elim (tdeq_fqup_trans … H43 … HT04) -T4 #L2 #T4 #H04 #HT43 #HL24
-      /4 width=7 by fsb_fpbs_trans, tdeq_lfdeq_lfpx_fpbs, fpbs_fqup_trans/
-    | elim (cpxs_tdneq_fwd_step_sn … HT04 HnT04) -HT04 -HnT04 #T2 #T5 #HT02 #HnT02 #HT25 #HT54
-      elim (fpbs_cpx_tdneq_trans … H10 … HT02 HnT02) -T0 #T0 #HT10 #HnT10 #H02
-      /3 width=14 by fpbs_cpxs_tdeq_fqup_lfpx_trans/
+    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/
     ]
   ]
 ]
 qed.
 
-lemma csx_fsb: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → ≥[h, o] 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,o. ∀R:relation3 genv lenv term.
-                   (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                               (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                               R G1 L1 T1
-                   ) →
-                   ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R G L T.
+lemma csx_ind_fpb (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_alt/ qed-.
 
-lemma csx_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
-                    (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                                (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                                R G1 L1 T1
-                    ) →
-                    ∀G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ → R 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-.