update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / csx_vector.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_vector.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_vector.ma
index d436de7742d1b12c7a2a43c65d2b1f669e0c3ca1..ab7046fd1719b2ae2c96081b9d7a8d0e1f19c02b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_vector.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_vector.ma
@@ -17,8 +17,8 @@ include "basic_2/rt_computation/csx.ma".
 
 (* STRONGLY NORMALIZING TERMS VECTORS FOR UNBOUND PARALLEL RT-TRANSITION ****)
 
-definition csxv: ∀h. relation3 genv lenv (list term) ≝
-                 λh,G,L. all … (csx h G L).
+definition csxv (h) (G) (L): predicate (list term) ≝
+           all … (csx h G L).
 
 interpretation
    "strong normalization for unbound context-sensitive parallel rt-transition (term vector)"
@@ -26,14 +26,16 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma csxv_inv_cons: ∀h,G,L,T,Ts. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T⨮Ts❫ →
-                     ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫ ∧ ❪G,L❫ ⊢ ⬈*[h] 𝐒❪Ts❫.
+lemma csxv_inv_cons (h) (G) (L):
+      ∀T,Ts. ❪G,L❫ ⊢ ⬈*𝐒[h] T⨮Ts →
+      ∧∧ ❪G,L❫ ⊢ ⬈*𝐒[h] T & ❪G,L❫ ⊢ ⬈*𝐒[h] Ts.
 normalize // qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma csx_fwd_applv: ∀h,G,L,T,Vs. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪ⒶVs.T❫ →
-                     ❪G,L❫ ⊢ ⬈*[h] 𝐒❪Vs❫ ∧ ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T❫.
+lemma csx_fwd_applv (h) (G) (L):
+      ∀T,Vs. ❪G,L❫ ⊢ ⬈*𝐒[h] ⒶVs.T →
+      ∧∧ ❪G,L❫ ⊢ ⬈*𝐒[h] Vs & ❪G,L❫ ⊢ ⬈*𝐒[h] T.
 #h #G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
 #V #Vs #IHVs #HVs
 lapply (csx_fwd_pair_sn … HVs) #HV