- commit of the "s_computation" component ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
index 54284a0b1e2dbeeeb1ccd1bd4ca7f566af9c88e1..e86c302b8217c848917bcad34c3c9ee1e5105131 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_csx.ma
@@ -18,23 +18,23 @@ include "basic_2/computation/csx_fpbs.ma".
 include "basic_2/computation/lsx_csx.ma".
 include "basic_2/computation/fsb_alt.ma".
 
-(* "QRST" STRONGLY NORMALIZING TERMS ****************************************)
+(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
 
 (* Advanced propreties on context-sensitive extended normalizing terms ******)
 
-lemma csx_fsb_fpbs: ∀h,g,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
-                    ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦥[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #L1 #T1 #H @(csx_ind … H) -T1
+lemma csx_fsb_fpbs: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 →
+                    ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦥[h, o] ⦃G2, L2, T2⦄.
+#h #o #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 (csx_fpbs_conf … H10) // -HT1
 #HT0 generalize in match IHu; -IHu generalize in match H10; -H10
 @(lsx_ind … (csx_lsx … HT0 0)) -L0
-#L0 #_ #IHl #H10 #IHu @fsb_intro
-#G2 #L2 #T2 * -G2 -L2 -T2 [ -IHl -IHc | -IHu -IHl |  ]
+#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_trans_neq … H10 … HT02 HnT02) -T0
   /3 width=4 by/
-| #L2 #HL02 #HnL02 @(IHl … HL02 HnL02) -IHl -HnL02 [ -IHu -IHc | ]
+| #L2 #HL02 #HnL02 @(IHd … HL02 HnL02) -IHd -HnL02 [ -IHu -IHc | ]
   [ /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/
   | #G3 #L3 #T3 #H03 #_ elim (lpx_fqup_trans … H03 … HL02) -L2
     #L4 #T4 elim (eq_term_dec T0 T4) [ -IHc | -IHu ]
@@ -48,23 +48,23 @@ lemma csx_fsb_fpbs: ∀h,g,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
 ]
 qed.
 
-lemma csx_fsb: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦥[h, g] ⦃G, L, T⦄.
+lemma csx_fsb: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦥[h, o] ⦃G, L, T⦄.
 /2 width=5 by csx_fsb_fpbs/ qed.
 
 (* Advanced eliminators *****************************************************)
 
-lemma csx_ind_fpb: ∀h,g. ∀R:relation3 genv lenv term.
-                   (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
-                               (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+lemma csx_ind_fpb: ∀h,o. ∀R:relation3 genv lenv term.
+                   (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] 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, g] T → R G L T.
+                   ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → R G L T.
 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
 
-lemma csx_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
-                    (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
-                                (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+lemma csx_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
+                    (∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] 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, g] T → R G L T.
+                    ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → R G L T.
 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.