matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpa/fpas_vector.etc

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  14
  15 include "basic_2/grammar/term_vector.ma".
  16 include "basic_2/multiple/fpas.ma".
  17
  18 (* MULTIPLE VECTOR AJUSTMENT ************************************************)
  19
  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)
  25 .
  26
  27 interpretation
  28    "multiple vector ajustment (restricted closure)"
  29    'RAjustStar L1 T1s s L2 T2s = (fpasv s L1 T1s L2 T2s).
  30
  31 (* Basic inversion lemmas ***************************************************)
  32
  33
  34
  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⦄ &
  38                                  X = Ⓐ V2s.T2.
  39 #L1 #L2 #V1s elim V1s -V1s
  40 [ #T1 #X #s #H
  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 *)
  46 ]
  47 qed-.
  48
  49 (* Basic properties *********************************************************)
  50
  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/
  56 qed.