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(*   Copyright Dominique Larchey-Wendling [*]                 *)
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(*                             [*] Affiliation LORIA -- CNRS  *)
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(*      This file is distributed under the terms of the       *)
(*         CeCILL v2 FREE SOFTWARE LICENSE AGREEMENT          *)
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(** ** Object-level encoding of exponential *)
Set Implicit Arguments.
Local Notation power := (mscal mult 1).
Local Notation expo := (mscal mult 1).

(* Specifications: *)
Theorem dio_rel_alpha a b c : 𝔻P a -> 𝔻P b -> 𝔻P c
-> 𝔻R (fun ν => 3 < b ν /\ a ν = alpha_nat (b ν) (c ν)).
Lemma dio_rel_is_digit c q i y : 𝔻P c -> 𝔻P q -> 𝔻P i -> 𝔻P y
-> 𝔻R (fun ν => is_digit (c ν) (q ν) (i ν) (y ν)).
Lemma dio_rel_binomial b n k : 𝔻P b -> 𝔻P n -> 𝔻P k
-> 𝔻R (fun ν => b ν = binomial (n ν) (k ν)).