- commit of the "s_computation" component ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
index ee557e4385fa4038a8df142dab4d8079c0f79c8a..b6c91c8b124135cc7625cb1789b3e4bf9e7a8748 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
@@ -19,56 +19,56 @@ include "basic_2/computation/lprs.ma".
 (* SN EXTENDED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *******************)
 
 definition lpxs: ∀h. sd h → relation3 genv lenv lenv ≝
-                 λh,g,G. TC … (lpx h g G).
+                 λh,o,G. TC … (lpx h o G).
 
 interpretation "extended parallel computation (local environment, sn variant)"
-   'PRedSnStar h g G L1 L2 = (lpxs h g G L1 L2).
+   'PRedSnStar h o G L1 L2 = (lpxs h o G L1 L2).
 
 (* Basic eliminators ********************************************************)
 
-lemma lpxs_ind: ∀h,g,G,L1. ∀R:predicate lenv. R L1 →
-                (∀L,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L → ⦃G, L⦄ ⊢ ➡[h, g] L2 → R L → R L2) →
-                ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → R L2.
-#h #g #G #L1 #R #HL1 #IHL1 #L2 #HL12
+lemma lpxs_ind: ∀h,o,G,L1. ∀R:predicate lenv. R L1 →
+                (∀L,L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L → ⦃G, L⦄ ⊢ ➡[h, o] L2 → R L → R L2) →
+                ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → R L2.
+#h #o #G #L1 #R #HL1 #IHL1 #L2 #HL12
 @(TC_star_ind … HL1 IHL1 … HL12) //
 qed-.
 
-lemma lpxs_ind_dx: ∀h,g,G,L2. ∀R:predicate lenv. R L2 →
-                   (∀L1,L. ⦃G, L1⦄ ⊢ ➡[h, g] L → ⦃G, L⦄ ⊢ ➡*[h, g] L2 → R L → R L1) →
-                   ∀L1. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → R L1.
-#h #g #G #L2 #R #HL2 #IHL2 #L1 #HL12
+lemma lpxs_ind_dx: ∀h,o,G,L2. ∀R:predicate lenv. R L2 →
+                   (∀L1,L. ⦃G, L1⦄ ⊢ ➡[h, o] L → ⦃G, L⦄ ⊢ ➡*[h, o] L2 → R L → R L1) →
+                   ∀L1. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → R L1.
+#h #o #G #L2 #R #HL2 #IHL2 #L1 #HL12
 @(TC_star_ind_dx … HL2 IHL2 … HL12) //
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lprs_lpxs: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
+lemma lprs_lpxs: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1⦄ ⊢ ➡*[h, o] L2.
 /3 width=3 by lpr_lpx, monotonic_TC/ qed.
 
-lemma lpx_lpxs: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
+lemma lpx_lpxs: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → ⦃G, L1⦄ ⊢ ➡*[h, o] L2.
 /2 width=1 by inj/ qed.
 
-lemma lpxs_refl: ∀h,g,G,L. ⦃G, L⦄ ⊢ ➡*[h, g] L.
+lemma lpxs_refl: ∀h,o,G,L. ⦃G, L⦄ ⊢ ➡*[h, o] L.
 /2 width=1 by lprs_lpxs/ qed.
 
-lemma lpxs_strap1: ∀h,g,G,L1,L,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L → ⦃G, L⦄ ⊢ ➡[h, g] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
+lemma lpxs_strap1: ∀h,o,G,L1,L,L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L → ⦃G, L⦄ ⊢ ➡[h, o] L2 → ⦃G, L1⦄ ⊢ ➡*[h, o] L2.
 /2 width=3 by step/ qed.
 
-lemma lpxs_strap2: ∀h,g,G,L1,L,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L → ⦃G, L⦄ ⊢ ➡*[h, g] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
+lemma lpxs_strap2: ∀h,o,G,L1,L,L2. ⦃G, L1⦄ ⊢ ➡[h, o] L → ⦃G, L⦄ ⊢ ➡*[h, o] L2 → ⦃G, L1⦄ ⊢ ➡*[h, o] L2.
 /2 width=3 by TC_strap/ qed.
 
-lemma lpxs_pair_refl: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ∀I,V. ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡*[h, g] L2.ⓑ{I}V.
+lemma lpxs_pair_refl: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → ∀I,V. ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡*[h, o] L2.ⓑ{I}V.
 /2 width=1 by TC_lpx_sn_pair_refl/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lpxs_inv_atom1: ∀h,g,G,L2. ⦃G, ⋆⦄ ⊢ ➡*[h, g] L2 → L2 = ⋆.
+lemma lpxs_inv_atom1: ∀h,o,G,L2. ⦃G, ⋆⦄ ⊢ ➡*[h, o] L2 → L2 = ⋆.
 /2 width=2 by TC_lpx_sn_inv_atom1/ qed-.
 
-lemma lpxs_inv_atom2: ∀h,g,G,L1. ⦃G, L1⦄ ⊢ ➡*[h, g] ⋆ → L1 = ⋆.
+lemma lpxs_inv_atom2: ∀h,o,G,L1. ⦃G, L1⦄ ⊢ ➡*[h, o] ⋆ → L1 = ⋆.
 /2 width=2 by TC_lpx_sn_inv_atom2/ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lpxs_fwd_length: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → |L1| = |L2|.
+lemma lpxs_fwd_length: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → |L1| = |L2|.
 /2 width=2 by TC_lpx_sn_fwd_length/ qed-.