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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 bounded universal quantification II *)
From Undecidability.Shared.Libs.DLW.Utils
From Undecidability.H10.Matija
From Undecidability.H10.Dio
Set Implicit Arguments.
Local Infix "≲" := binary_le (at level 70, no associativity).
Local Notation power := (mscal mult 1).
Local Notation "∑" := (msum plus 0).
Local Infix "⇣" := nat_meet (at level 40, left associativity).
Local Infix "⇡" := nat_join (at level 50, left associativity).
(* seqs_of_ones l q u u1 iff  l+1 < q and  u  = ∑(i<l) r^(2^(1+i)) and  u1 = ∑(i<l) r^(2^(2+i)) with r := 2^(4q)  *)

Theorem dio_rel_seqs_of_ones l q u u1 : 𝔻F l -> 𝔻F q -> 𝔻F u -> 𝔻F u1
-> 𝔻R (fun v => seqs_of_ones (l v) (q v) (u v) (u1 v)).