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15 include "basic_2/rt_equivalence/cpcs_cprs.ma".
16 include "basic_2/dynamic/cnv_preserve.ma".
18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
20 (* Forward lemmas with r-equivalence ****************************************)
22 lemma cnv_cpms_conf_eq (h) (a) (n) (G) (L):
23 ∀T. ❨G,L❩ ⊢ T ![h,a] →
24 ∀T1. ❨G,L❩ ⊢ T ➡*[h,n] T1 → ∀T2. ❨G,L❩ ⊢ T ➡*[h,n] T2 → ❨G,L❩ ⊢ T1 ⬌*[h] T2.
25 #h #a #n #G #L #T #HT #T1 #HT1 #T2 #HT2
26 elim (cnv_cpms_conf … HT … HT1 … HT2) -T <minus_n_n #T #HT1 #HT2
27 /2 width=3 by cprs_div/
30 lemma cnv_cpms_fwd_appl_sn_decompose (h) (a) (G) (L):
31 ∀V,T. ❨G,L❩ ⊢ ⓐV.T ![h,a] → ∀n,X. ❨G,L❩ ⊢ ⓐV.T ➡*[h,n] X →
32 ∃∃U. ❨G,L❩ ⊢ T ![h,a] & ❨G,L❩ ⊢ T ➡*[h,n] U & ❨G,L❩ ⊢ ⓐV.U ⬌*[h] X.
33 #h #a #G #L #V #T #H0 #n #X #HX
34 elim (cnv_inv_appl … H0) #m #p #W #U #_ #_ #HT #_ #_ -m -p -W -U
35 elim (cnv_fwd_cpms_total h … n … HT) #U #HTU
36 lapply (cpms_appl_dx … V V … HTU) [ // ] #H
37 /3 width=8 by cnv_cpms_conf_eq, ex3_intro/