(* 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)"
(* 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