(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERM VECTORS *************)
definition csxv: ∀h. sd h → relation3 genv lenv (list term) ≝
- λh,g,G,L. all … (csx h g G L).
+ λh,o,G,L. all … (csx h o G L).
interpretation
"context-sensitive strong normalization (term vector)"
- 'SN h g G L Ts = (csxv h g G L Ts).
+ 'SN h o G L Ts = (csxv h o G L Ts).
(* Basic inversion lemmas ***************************************************)
-lemma csxv_inv_cons: ∀h,g,G,L,T,Ts. ⦃G, L⦄ ⊢ ⬊*[h, g] T @ Ts →
- ⦃G, L⦄ ⊢ ⬊*[h, g] T ∧ ⦃G, L⦄ ⊢ ⬊*[h, g] Ts.
+lemma csxv_inv_cons: ∀h,o,G,L,T,Ts. ⦃G, L⦄ ⊢ ⬊*[h, o] T @ Ts →
+ ⦃G, L⦄ ⊢ ⬊*[h, o] T ∧ ⦃G, L⦄ ⊢ ⬊*[h, o] Ts.
normalize // qed-.
(* Basic forward lemmas *****************************************************)
-lemma csx_fwd_applv: ∀h,g,G,L,T,Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Ⓐ Vs.T →
- ⦃G, L⦄ ⊢ ⬊*[h, g] Vs ∧ ⦃G, L⦄ ⊢ ⬊*[h, g] T.
-#h #g #G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
+lemma csx_fwd_applv: ∀h,o,G,L,T,Vs. ⦃G, L⦄ ⊢ ⬊*[h, o] Ⓐ Vs.T →
+ ⦃G, L⦄ ⊢ ⬊*[h, o] Vs ∧ ⦃G, L⦄ ⊢ ⬊*[h, o] T.
+#h #o #G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
#V #Vs #IHVs #HVs
lapply (csx_fwd_pair_sn … HVs) #HV
lapply (csx_fwd_flat_dx … HVs) -HVs #HVs