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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/static/lfeq_lreq.ma".
16 include "basic_2/static/aaa.ma".
18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
20 (* Properties with equivalence on referred entries **************************)
22 lemma lfeq_aaa_trans: ∀G,L2,T,A. ⦃G, L2⦄ ⊢ T ⁝ A →
23 ∀L1. L1 ≡[T] L2 → ⦃G, L1⦄ ⊢ T ⁝ A.
24 #G #L2 #T #A #H elim H -G -L2 -T -A /2 width=1 by aaa_sort/
25 [ #I #G #L2 #V2 #A #_ #IH #L1 #H
26 elim (lfeq_inv_zero_pair_dx … H) -H /3 width=1 by aaa_zero/
27 | #I #G #L2 #V2 #A #i #_ #IH #L1 #H
28 elim (lfeq_inv_lref_pair_dx … H) -H /3 width=1 by aaa_lref/
29 | #p #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H
30 elim (lfeq_inv_bind … H) -H /3 width=2 by aaa_abbr/
31 | #p #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H
32 elim (lfeq_inv_bind … H) -H /3 width=1 by aaa_abst/
33 | #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H
34 elim (lfeq_inv_flat … H) -H /3 width=3 by aaa_appl/
35 | #G #L2 #V #T #A #_ #_ #IHV #IHT #L1 #H
36 elim (lfeq_inv_flat … H) -H /3 width=1 by aaa_cast/
40 lemma aaa_lfeq_conf: ∀G,L2,T,A. ⦃G, L2⦄ ⊢ T ⁝ A →
41 ∀L1. L2 ≡[T] L1 → ⦃G, L1⦄ ⊢ T ⁝ A.
42 /3 width=3 by lfeq_aaa_trans, lfeq_sym/ qed-.