- commit of the "s_computation" component ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/scpds.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/scpds.ma
index 87fe99592664707790032e6cfa72c6756c0b490b..1f189c15e2830d554850bd9fe2deed4cf8bc7e3d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/scpds.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/scpds.ma
@@ -19,30 +19,30 @@ include "basic_2/computation/cprs.ma".
 (* STRATIFIED DECOMPOSED PARALLEL COMPUTATION ON TERMS **********************)
 
 definition scpds: ∀h. sd h → nat → relation4 genv lenv term term ≝
-                  λh,g,l2,G,L,T1,T2.
-                  ∃∃T,l1. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, l2] T & ⦃G, L⦄ ⊢ T ➡* T2.
+                  λh,o,d2,G,L,T1,T2.
+                  ∃∃T,d1. d2 ≤ d1 & ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 & ⦃G, L⦄ ⊢ T1 •*[h, d2] T & ⦃G, L⦄ ⊢ T ➡* T2.
 
 interpretation "stratified decomposed parallel computation (term)"
-   'DPRedStar h g l G L T1 T2 = (scpds h g l G L T1 T2).
+   'DPRedStar h o d G L T1 T2 = (scpds h o d G L T1 T2).
 
 (* Basic properties *********************************************************)
 
-lemma sta_cprs_scpds: ∀h,g,G,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T1 •*[h, 1] T →
-                      ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 1] T2.
+lemma sta_cprs_scpds: ∀h,o,G,L,T1,T,T2,d. ⦃G, L⦄ ⊢ T1 ▪[h, o] d+1 → ⦃G, L⦄ ⊢ T1 •*[h, 1] T →
+                      ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, 1] T2.
 /2 width=6 by ex4_2_intro/ qed.
 
-lemma lstas_scpds: ∀h,g,G,L,T1,T2,l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 →
-                   ∀l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 •*[h, l2] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l2] T2.
+lemma lstas_scpds: ∀h,o,G,L,T1,T2,d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 →
+                   ∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d2] T2.
 /2 width=6 by ex4_2_intro/ qed.
 
-lemma scpds_strap1: ∀h,g,G,L,T1,T,T2,l.
-                    ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, l] T2.
-#h #g #G #L #T1 #T #T2 #l * /3 width=8 by cprs_strap1, ex4_2_intro/
+lemma scpds_strap1: ∀h,o,G,L,T1,T,T2,d.
+                    ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d] T2.
+#h #o #G #L #T1 #T #T2 #d * /3 width=8 by cprs_strap1, ex4_2_intro/
 qed.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma scpds_fwd_cprs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 0] T2 →
+lemma scpds_fwd_cprs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, o, 0] T2 →
                       ⦃G, L⦄ ⊢ T1 ➡* T2.
-#h #g #G #L #T1 #T2 * /3 width=3 by cprs_strap2, lstas_cpr/
+#h #o #G #L #T1 #T2 * /3 width=3 by cprs_strap2, lstas_cpr/
 qed-.