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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/rt_equivalence/cpcs_cprs.ma".
16 include "basic_2/i_dynamic/ntas.ma".
18 (* ITERATED NATIVE TYPE ASSIGNMENT FOR TERMS ********************************)
20 (* Properties with r-equivalence for terms **********************************)
22 lemma ntas_zero (h) (a) (G) (L):
23 ∀T1,T2. ❨G,L❩ ⊢ T1 ![h,a] → ❨G,L❩ ⊢ T2 ![h,a] → ❨G,L❩ ⊢ T1 ⬌*[h] T2 → ❨G,L❩ ⊢ T1 :*[h,a,0] T2.
24 #h #a #G #L #T1 #T2 #HT1 #HT2 #H
25 elim (cpcs_inv_cprs … H) -H #T0 #HT10 #HT20
26 /2 width=3 by ntas_intro/
29 (* Inversion lemmas with r-equivalence for terms ****************************)
31 lemma ntas_inv_zero (h) (a) (G) (L):
32 ∀T1,T2. ❨G,L❩ ⊢ T1 :*[h,a,0] T2 →
33 ∧∧ ❨G,L❩ ⊢ T1 ![h,a] & ❨G,L❩ ⊢ T2 ![h,a] & ❨G,L❩ ⊢ T1 ⬌*[h] T2.
34 #h #a #G #L #T1 #T2 * #T0 #HT1 #HT2 #HT20 #HT10
35 /3 width=3 by cprs_div, and3_intro/