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15 include "basic_2/rt_conversion/lpce.ma".
16 include "basic_2/dynamic/cnv.ma".
18 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
20 theorem cnv_cpce_trans_lpce (h) (G):
21 ∀L1,T1,T2. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T2 → ⦃G,L1⦄ ⊢ T1 !*[h] →
22 ∀L2. ⦃G,L1⦄ ⊢ ⬌η[h] L2 → ⦃G,L2⦄ ⊢ T2 !*[h].
23 #h #G #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2
24 [ #G #L1 #s #_ #L2 #_ //
25 | #G #K1 #V1 #_ #Y2 #HY
26 elim (lpce_inv_pair_sn … HY) -HY #K2 #V2 #HK #HV #H destruct