milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/dxprs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/dxprs.ma
index 1db0aec2bd2213fa3804bd48449c5d286c7e4f7b..3f2b0fb099a991b6461c9d7088209ac4e6561997 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/dxprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/dxprs.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unwind/sstas.ma".
+include "basic_2/unfold/sstas.ma".
 include "basic_2/computation/cprs.ma".
 
 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
@@ -21,19 +21,18 @@ definition dxprs: ∀h. sd h → lenv → relation term ≝ λh,g,L,T1,T2.
                   ∃∃T. ⦃h, L⦄ ⊢ T1 •*[g] T & L ⊢ T ➡* T2.
 
 interpretation "decomposed extended parallel computation (term)"
-   'DecomposedXPRedStar h g L T1 T2 = (dxprs h g L T1 T2).
+   'DecomposedPRedStar h g L T1 T2 = (dxprs h g L T1 T2).
 
 (* Basic properties *********************************************************)
 
-lemma dxprs_refl: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → ⦃h, L⦄ ⊢ T •*➡*[g] T.
-/3 width=3/ qed.
+lemma dxprs_refl: ∀h,g,L. reflexive … (dxprs h g L).
+/2 width=3/ qed.
 
 lemma sstas_dxprs: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
 /2 width=3/ qed.
 
-lemma cprs_dxprs: ∀h,g,L,T1,T2,U,l. ⦃h, L⦄ ⊢ T1 •[g, l] U → L ⊢ T1 ➡* T2 →
-                  ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
-/3 width=3/ qed.
+lemma cprs_dxprs: ∀h,g,L,T1,T2.  L ⊢ T1 ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
+/2 width=3/ qed.
 
 lemma dxprs_strap1: ∀h,g,L,T1,T,T2.
                     ⦃h, L⦄ ⊢ T1 •*➡*[g] T → L ⊢ T ➡ T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
@@ -41,6 +40,20 @@ lemma dxprs_strap1: ∀h,g,L,T1,T,T2.
 qed.
 
 lemma dxprs_strap2: ∀h,g,L,T1,T,T2,l.
-                    ⦃h, L⦄ ⊢ T1 •[g, l+1] T → ⦃h, L⦄ ⊢ T •*➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
+                    ⦃h, L⦄ ⊢ T1 •[g] ⦃l+1, T⦄ → ⦃h, L⦄ ⊢ T •*➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
 #h #g #L #T1 #T #T2 #l #HT1 * /3 width=4/
 qed.
+
+lemma ssta_cprs_dxprs: ∀h,g,L,T1,T,T2,l. ⦃h, L⦄ ⊢ T1 •[g] ⦃l+1, T⦄ →
+                       L ⊢ T ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
+/3 width=3/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma dxprs_inv_abst1: ∀h,g,a,L,V1,T1,U2. ⦃h, L⦄ ⊢ ⓛ{a}V1. T1 •*➡*[g] U2 →
+                       ∃∃V2,T2. L ⊢ V1 ➡* V2 & ⦃h, L.ⓛV1⦄ ⊢ T1 •*➡*[g] T2 &
+                                U2 = ⓛ{a}V2. T2.
+#h #g #a #L #V1 #T1 #U2 * #X #H1 #H2
+elim (sstas_inv_bind1 … H1) -H1 #U #HTU1 #H destruct
+elim (cprs_fwd_abst1 … H2 Abst V1) -H2 #V2 #T2 #HV12 #HUT2 #H destruct /3 width=5/
+qed-.