- commit of the "s_computation" component ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_alt.ma
index 05637c0e72c4bcd66888495961e0255ae3ea4e65..07f3d94b27695861144972ce102b7cd5f16c4458 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lsx_alt.ma
@@ -20,54 +20,54 @@ include "basic_2/computation/lsx.ma".
 
 (* alternative definition of lsx *)
 definition lsxa: ∀h. sd h → relation4 ynat term genv lenv ≝
-                 λh,g,l,T,G. SN … (lpxs h g G) (lleq l T).
+                 λh,o,l,T,G. SN … (lpxs h o G) (lleq l T).
 
 interpretation
    "extended strong normalization (local environment) alternative"
-   'SNAlt h g l T G L = (lsxa h g T l G L).
+   'SNAlt h o l T G L = (lsxa h o T l G L).
 
 (* Basic eliminators ********************************************************)
 
-lemma lsxa_ind: ∀h,g,G,T,l. ∀R:predicate lenv.
-                (∀L1. G ⊢ ⬊⬊*[h, g, T, l] L1 →
-                      (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ≡[T, l] L2 → ⊥) → R L2) →
+lemma lsxa_ind: ∀h,o,G,T,l. ∀R:predicate lenv.
+                (∀L1. G ⊢ ⬊⬊*[h, o, T, l] L1 →
+                      (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → R L2) →
                       R L1
                 ) →
-                ∀L. G ⊢ ⬊⬊*[h, g, T, l] L → R L.
-#h #g #G #T #l #R #H0 #L1 #H elim H -L1
+                ∀L. G ⊢ ⬊⬊*[h, o, T, l] L → R L.
+#h #o #G #T #l #R #H0 #L1 #H elim H -L1
 /5 width=1 by lleq_sym, SN_intro/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsxa_intro: ∀h,g,G,L1,T,l.
-                  (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, g, T, l] L2) →
-                  G ⊢ ⬊⬊*[h, g, T, l] L1.
+lemma lsxa_intro: ∀h,o,G,L1,T,l.
+                  (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, o, T, l] L2) →
+                  G ⊢ ⬊⬊*[h, o, T, l] L1.
 /5 width=1 by lleq_sym, SN_intro/ qed.
 
-fact lsxa_intro_aux: ∀h,g,G,L1,T,l.
-                     (∀L,L2. ⦃G, L⦄ ⊢ ➡*[h, g] L2 → L1 ≡[T, l] L → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, g, T, l] L2) →
-                     G ⊢ ⬊⬊*[h, g, T, l] L1.
+fact lsxa_intro_aux: ∀h,o,G,L1,T,l.
+                     (∀L,L2. ⦃G, L⦄ ⊢ ➡*[h, o] L2 → L1 ≡[T, l] L → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, o, T, l] L2) →
+                     G ⊢ ⬊⬊*[h, o, T, l] L1.
 /4 width=3 by lsxa_intro/ qed-.
 
-lemma lsxa_lleq_trans: ∀h,g,T,G,L1,l. G ⊢ ⬊⬊*[h, g, T, l] L1 →
-                       ∀L2. L1 ≡[T, l] L2 → G ⊢ ⬊⬊*[h, g, T, l] L2.
-#h #g #T #G #L1 #l #H @(lsxa_ind … H) -L1
+lemma lsxa_lleq_trans: ∀h,o,T,G,L1,l. G ⊢ ⬊⬊*[h, o, T, l] L1 →
+                       ∀L2. L1 ≡[T, l] L2 → G ⊢ ⬊⬊*[h, o, T, l] L2.
+#h #o #T #G #L1 #l #H @(lsxa_ind … H) -L1
 #L1 #_ #IHL1 #L2 #HL12 @lsxa_intro
 #K2 #HLK2 #HnLK2 elim (lleq_lpxs_trans … HLK2 … HL12) -HLK2
 /5 width=4 by lleq_canc_sn, lleq_trans/
 qed-.
 
-lemma lsxa_lpxs_trans: ∀h,g,T,G,L1,l. G ⊢ ⬊⬊*[h, g, T, l] L1 →
-                       ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → G ⊢ ⬊⬊*[h, g, T, l] L2.
-#h #g #T #G #L1 #l #H @(lsxa_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
+lemma lsxa_lpxs_trans: ∀h,o,T,G,L1,l. G ⊢ ⬊⬊*[h, o, T, l] L1 →
+                       ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → G ⊢ ⬊⬊*[h, o, T, l] L2.
+#h #o #T #G #L1 #l #H @(lsxa_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
 elim (lleq_dec T L1 L2 l) /3 width=4 by lsxa_lleq_trans/
 qed-.
 
-lemma lsxa_intro_lpx: ∀h,g,G,L1,T,l.
-                      (∀L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, g, T, l] L2) →
-                      G ⊢ ⬊⬊*[h, g, T, l] L1.
-#h #g #G #L1 #T #l #IH @lsxa_intro_aux
+lemma lsxa_intro_lpx: ∀h,o,G,L1,T,l.
+                      (∀L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊⬊*[h, o, T, l] L2) →
+                      G ⊢ ⬊⬊*[h, o, T, l] L1.
+#h #o #G #L1 #T #l #IH @lsxa_intro_aux
 #L #L2 #H @(lpxs_ind_dx … H) -L
 [ #H destruct #H elim H //
 | #L0 #L elim (lleq_dec T L1 L l) /3 width=1 by/
@@ -79,37 +79,37 @@ qed-.
 
 (* Main properties **********************************************************)
 
-theorem lsx_lsxa: ∀h,g,G,L,T,l. G ⊢ ⬊*[h, g, T, l] L → G ⊢ ⬊⬊*[h, g, T, l] L.
-#h #g #G #L #T #l #H @(lsx_ind … H) -L
+theorem lsx_lsxa: ∀h,o,G,L,T,l. G ⊢ ⬊*[h, o, T, l] L → G ⊢ ⬊⬊*[h, o, T, l] L.
+#h #o #G #L #T #l #H @(lsx_ind … H) -L
 /4 width=1 by lsxa_intro_lpx/
 qed.
 
 (* Main inversion lemmas ****************************************************)
 
-theorem lsxa_inv_lsx: ∀h,g,G,L,T,l. G ⊢ ⬊⬊*[h, g, T, l] L → G ⊢ ⬊*[h, g, T, l] L.
-#h #g #G #L #T #l #H @(lsxa_ind … H) -L
+theorem lsxa_inv_lsx: ∀h,o,G,L,T,l. G ⊢ ⬊⬊*[h, o, T, l] L → G ⊢ ⬊*[h, o, T, l] L.
+#h #o #G #L #T #l #H @(lsxa_ind … H) -L
 /4 width=1 by lsx_intro, lpx_lpxs/
 qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma lsx_intro_alt: ∀h,g,G,L1,T,l.
-                     (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊*[h, g, T, l] L2) →
-                     G ⊢ ⬊*[h, g, T, l] L1.
+lemma lsx_intro_alt: ∀h,o,G,L1,T,l.
+                     (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → G ⊢ ⬊*[h, o, T, l] L2) →
+                     G ⊢ ⬊*[h, o, T, l] L1.
 /6 width=1 by lsxa_inv_lsx, lsx_lsxa, lsxa_intro/ qed.
 
-lemma lsx_lpxs_trans: ∀h,g,G,L1,T,l. G ⊢ ⬊*[h, g, T, l] L1 →
-                      ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → G ⊢ ⬊*[h, g, T, l] L2.
+lemma lsx_lpxs_trans: ∀h,o,G,L1,T,l. G ⊢ ⬊*[h, o, T, l] L1 →
+                      ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → G ⊢ ⬊*[h, o, T, l] L2.
 /4 width=3 by lsxa_inv_lsx, lsx_lsxa, lsxa_lpxs_trans/ qed-.
 
 (* Advanced eliminators *****************************************************)
 
-lemma lsx_ind_alt: ∀h,g,G,T,l. ∀R:predicate lenv.
-                   (∀L1. G ⊢ ⬊*[h, g, T, l] L1 →
-                         (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → (L1 ≡[T, l] L2 → ⊥) → R L2) →
+lemma lsx_ind_alt: ∀h,o,G,T,l. ∀R:predicate lenv.
+                   (∀L1. G ⊢ ⬊*[h, o, T, l] L1 →
+                         (∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → (L1 ≡[T, l] L2 → ⊥) → R L2) →
                          R L1
                    ) →
-                   ∀L. G ⊢ ⬊*[h, g, T, l] L → R L.
-#h #g #G #T #l #R #IH #L #H @(lsxa_ind h g G T l … L)
+                   ∀L. G ⊢ ⬊*[h, o, T, l] L → R L.
+#h #o #G #T #l #R #IH #L #H @(lsxa_ind h o G T l … L)
 /4 width=1 by lsxa_inv_lsx, lsx_lsxa/
 qed-.