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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_2A/substitution/lift_vector.ma".
16 include "basic_2A/multiple/lifts.ma".
18 (* GENERIC TERM VECTOR RELOCATION *******************************************)
20 inductive liftsv (cs:mr2) : relation (list term) ≝
21 | liftsv_nil : liftsv cs (ⓔ) (ⓔ)
22 | liftsv_cons: ∀T1s,T2s,T1,T2.
23 ⬆*[cs] T1 ≡ T2 → liftsv cs T1s T2s →
24 liftsv cs (T1 ⨮ T1s) (T2 ⨮ T2s)
27 interpretation "generic relocation (vector)"
28 'RLiftStar cs T1s T2s = (liftsv cs T1s T2s).
30 (* Basic inversion lemmas ***************************************************)
32 lemma lifts_inv_applv1: ∀V1s,U1,T2,cs. ⬆*[cs] Ⓐ V1s. U1 ≡ T2 →
33 ∃∃V2s,U2. ⬆*[cs] V1s ≡ V2s & ⬆*[cs] U1 ≡ U2 &
35 #V1s elim V1s -V1s normalize
37 @ex3_2_intro [3,4: // |1,2: skip | // ] (**) (* explicit constructor *)
38 | #V1 #V1s #IHV1s #T1 #X #cs #H
39 elim (lifts_inv_flat1 … H) -H #V2 #Y #HV12 #HY #H destruct
40 elim (IHV1s … HY) -IHV1s -HY #V2s #T2 #HV12s #HT12 #H destruct
41 @(ex3_2_intro) [4: // |3: /2 width=2 by liftsv_cons/ |1,2: skip | // ] (**) (* explicit constructor *)
45 (* Basic properties *********************************************************)
47 lemma lifts_applv: ∀V1s,V2s,cs. ⬆*[cs] V1s ≡ V2s →
48 ∀T1,T2. ⬆*[cs] T1 ≡ T2 →
49 ⬆*[cs] Ⓐ V1s. T1 ≡ Ⓐ V2s. T2.
50 #V1s #V2s #cs #H elim H -V1s -V2s /3 width=1 by lifts_flat/