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15 include "basic_2/rt_computation/cpmuwe_csx.ma".
16 include "basic_2/rt_equivalence/cpes.ma".
17 include "basic_2/dynamic/cnv_preserve.ma".
19 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
21 (* Properties with t-unbound whd evaluation on terms ************************)
23 lemma cnv_cpmuwe_trans (h) (a) (G) (L):
24 ∀T1. ❨G,L❩ ⊢ T1 ![h,a] →
25 ∀n,T2. ❨G,L❩ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ❨G,L❩ ⊢ T2 ![h,a].
26 /3 width=4 by cpmuwe_fwd_cpms, cnv_cpms_trans/ qed-.
28 lemma cnv_R_cpmuwe_total (h) (a) (G) (L):
29 ∀T1. ❨G,L❩ ⊢ T1 ![h,a] → ∃n. R_cpmuwe h G L T1 n.
30 /4 width=3 by cnv_fwd_fsb, fsb_inv_csx, R_cpmuwe_total_csx/ qed-.
32 (* Main inversions with head evaluation for t-bound rt-transition on terms **)
34 theorem cnv_cpmuwe_mono (h) (a) (G) (L):
35 ∀T0. ❨G,L❩ ⊢ T0 ![h,a] →
36 ∀n1,T1. ❨G,L❩ ⊢ T0 ➡*𝐍𝐖*[h,n1] T1 →
37 ∀n2,T2. ❨G,L❩ ⊢ T0 ➡*𝐍𝐖*[h,n2] T2 →
38 ∧∧ ❨G,L❩ ⊢ T1 ⬌*[h,n2-n1,n1-n2] T2 & T1 ≃ T2.
39 #h #a #G #L #T0 #HT0 #n1 #T1 * #HT01 #HT1 #n2 #T2 * #HT02 #HT2
40 elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
41 /4 width=4 by cpms_div, teqw_canc_dx, conj/