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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_2/grammar/term_vector.ma".
16 include "basic_2/multiple/fpas.ma".
18 (* MULTIPLE VECTOR AJUSTMENT ************************************************)
20 inductive fpasv (s:bool): bi_relation lenv (list term) ≝
21 | fpasv_nil : ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ → fpasv s L1 (◊) L2 (◊)
22 | fpasv_cons: ∀L1,L2,T1s,T2s,T1,T2. ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ →
23 fpasv s L1 T1s L2 T2s →
24 fpasv s L1 (T1 @ T1s) L2 (T2 @ T2s)
28 "multiple vector ajustment (restricted closure)"
29 'RAjustStar L1 T1s s L2 T2s = (fpasv s L1 T1s L2 T2s).
31 (* Basic inversion lemmas ***************************************************)
35 (* Basic_1: was just: lifts1_flat (left to right) *)
36 lemma fpas_inv_applv1: ∀L1,L2,V1s,T1,X,s. ⦃L1, Ⓐ V1s.T1⦄ ⇳*[s] ⦃L2, X⦄ →
37 ∃∃V2s,T2. ⦃L1, V1s⦄ ⇳*[s] ⦃L2, V2s⦄ & ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄ &
39 #L1 #L2 #V1s elim V1s -V1s
41 @(ex3_2_intro … (◊) X) /2 width=3 by fpasv_nil/ (**) (* explicit constructor *)
42 | #V1 #V1s #IHV1s #T1 #X #s #H
43 elim (lifts_inv_flat1 … H) -H #V2 #Y #HV12 #HY #H destruct
44 elim (IHV1s … HY) -IHV1s -HY #V2s #T2 #HV12s #HT12 #H destruct
45 @(ex3_2_intro) [4: // |3: /2 width=2 by liftsv_cons/ |1,2: skip | // ] (**) (* explicit constructor *)
49 (* Basic properties *********************************************************)
51 (* Basic_1: was just: lifts1_flat (right to left) *)
52 lemma lifts_applv: ∀V1s,V2s,des. ⇧*[des] V1s ≡ V2s →
53 ∀T1,T2. ⇧*[des] T1 ≡ T2 →
54 ⇧*[des] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.
55 #V1s #V2s #des #H elim H -V1s -V2s /3 width=1 by lifts_flat/