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4 (* ||A|| A project by Andrea Asperti *)
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15 include "basic_2/rt_computation/cpms_cnu.ma".
16 include "basic_2/rt_computation/cpue.ma".
17 include "basic_2/dynamic/cnv_preserve.ma".
19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
21 (* Properties with evaluation for t-unbound rt-transition on terms **********)
23 lemma cnv_cpue_trans (a) (h) (G) (L):
24 ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
25 ∀T2. ⦃G,L⦄ ⊢ T1 ⥲*[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T2 ![a,h].
26 #a #h #G #L #T1 #HT1 #T2 * #n #HT12 #_
27 /2 width=4 by cnv_cpms_trans/
30 lemma cnv_cpue_cpms_conf (a) (h) (n) (G) (L):
31 ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1. ⦃G,L⦄ ⊢ T0 ➡*[n,h] T1 →
32 ∀T2. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T2⦄ →
33 ∃∃T. ⦃G,L⦄ ⊢ T1 ⥲*[h] 𝐍⦃T⦄ & T2 ≅ T.
34 #a #h #n1 #G #L #T0 #HT0 #T1 #HT01 #T2 * #n2 #HT02 #HT2
35 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
36 lapply (cpms_inv_cnu_sn … HT20 HT2) -HT20 #HT20
37 /4 width=8 by cnu_tueq_trans, ex2_intro/
40 (* Main properties with evaluation for t-unbound rt-transition on terms *****)
42 theorem cnv_cpue_mono (a) (h) (G) (L):
43 ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T1⦄ →
44 ∀T2. ⦃G,L⦄ ⊢ T0 ⥲*[h] 𝐍⦃T2⦄ → T1 ≅ T2.
45 #a #h #G #L #T0 #HT0 #T1 * #n1 #HT01 #HT1 #T2 * #n2 #HT02 #HT2
46 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
47 /3 width=8 by cpms_inv_cnu_sn, tueq_canc_dx/