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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2A/static/aaa_lift.ma".
16 include "basic_2A/static/da.ma".
18 (* DEGREE ASSIGNMENT FOR TERMS **********************************************)
20 (* Properties on atomic arity assignment for terms **************************)
22 lemma aaa_da: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∃d. ⦃G, L⦄ ⊢ T ▪[h, g] d.
23 #h #g #G #L #T #A #H elim H -G -L -T -A
24 [ #G #L #k elim (deg_total h g k) /3 width=2 by da_sort, ex_intro/
25 | * #G #L #K #V #B #i #HLK #_ * /3 width=5 by da_ldef, da_ldec, ex_intro/
26 | #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by da_bind, ex_intro/
27 | #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by da_bind, ex_intro/
28 | #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by da_flat, ex_intro/
29 | #G #L #W #T #A #_ #_ #_ * /3 width=2 by da_flat, ex_intro/