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14
15 include "basic_2/grammar/term_vector.ma".
16 include "basic_2/computation/csn.ma".
17
18 (* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERM VECTORS *************)
19
20 definition csnv: ∀h. sd h → relation3 genv lenv (list term) ≝
21                  λh,g,G,L. all … (csn h g G L).
22
23 interpretation
24    "context-sensitive strong normalization (term vector)"
25    'SN h g G L Ts = (csnv h g G L Ts).
26
27 (* Basic inversion lemmas ***************************************************)
28
29 lemma csnv_inv_cons: ∀h,g,G,L,T,Ts. ⦃G, L⦄ ⊢ ⬊*[h, g] T @ Ts →
30                      ⦃G, L⦄ ⊢ ⬊*[h, g] T ∧ ⦃G, L⦄ ⊢ ⬊*[h, g] Ts.
31 normalize // qed-.
32
33 (* Basic forward lemmas *****************************************************)
34
35 lemma csn_fwd_applv: ∀h,g,G,L,T,Vs. ⦃G, L⦄ ⊢ ⬊*[h, g] Ⓐ Vs.T →
36                      ⦃G, L⦄ ⊢ ⬊*[h, g] Vs ∧ ⦃G, L⦄ ⊢ ⬊*[h, g] T.
37 #h #g #G #L #T #Vs elim Vs -Vs /2 width=1/
38 #V #Vs #IHVs #HVs
39 lapply (csn_fwd_pair_sn … HVs) #HV
40 lapply (csn_fwd_flat_dx … HVs) -HVs #HVs
41 elim (IHVs HVs) -IHVs -HVs /3 width=1/
42 qed-.