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4 (* ||A|| A project by Andrea Asperti *)
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15 include "static_2/syntax/teqw_simple.ma".
16 include "basic_2/rt_computation/cpms_cpms.ma".
17 include "basic_2/rt_computation/cnuw.ma".
19 (* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
21 (* Advanced properties with simple terms ************************************)
23 lemma cnuw_appl_simple (h) (G) (L):
24 ∀V,T. 𝐒❨T❩ → ❨G,L❩ ⊢ ➡𝐍𝐖*[h] T → ❨G,L❩ ⊢ ➡𝐍𝐖*[h] ⓐV.T.
25 #h #G #L #V1 #T1 #H1T1 #H2T1 #n #X #H
26 elim (cpms_inv_appl_sn … H) -H *
27 [ #V2 #T2 #_ #HT12 #H destruct -H1T1
28 /3 width=2 by teqw_appl/
29 | #n1 #n2 #p #V2 #T2 #HT12 #_ #_ -n -n2
30 lapply (H2T1 … HT12) -H2T1 -n1 #H
31 lapply (teqw_simple_trans … H H1T1) -H -H1T1 #H
32 elim (simple_inv_bind … H)
33 | #n1 #n2 #p #V2 #W2 #W #T2 #_ #_ #HT12 #_ #_ -n -n2 -V2 -W2
34 lapply (H2T1 … HT12) -H2T1 -n1 #H
35 lapply (teqw_simple_trans … H H1T1) -H -H1T1 #H
36 elim (simple_inv_bind … H)