Removed outdated BAC2017 example.
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theory BAC2017
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imports "Isabelle_DOF.mathex_onto"
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Deriv
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Transcendental
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begin
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open_monitor*[exam::MathExam]
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(* currently rethinking on "deep ontologies" necessary ... Achim
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text*[idir::Author,affiliation="''LRI, CentraleSupelec''",
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email="''idir.aitsadoune@centralesupelec.fr''"]
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{*Idir AIT SADOUNE*}
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text*[keller::Author,affiliation="''LRI, Univ. Paris-Sud''",
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email="''Chantal.Keller@lri.fr''"]
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{*Chantal KELLER*}
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text{* This example is an excerpt from the french baccaleareat 2017.
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The textual explanations were kept in french.
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*}
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*)
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text*[header::Header,examSubject="[analysis,geometry]", date="''21-06-2017''",
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timeAllowed="240::int"]{* BACCALAUREAT GENERAL MATHEMATIQUES *}
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text{*
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\begin{itemize}
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\item Les calculatrices électroniques de poche sont autorisées, conformément à la réglementation
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en vigueur.
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\item Le sujet est composé de 4 exercices indépendants.
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\item Le candidat doit traiter tous les exercices.
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\item Le candidat est invité à faire figurer sur la copie toute trace de recherche, même incomplète
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ou non fructueuse, qu’il aura développée.
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\item Il est rappelé que la qualité de la rédaction, la clarté et la précision des raisonnements
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entreront pour une part importante dans l’appréciation des copies.
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\end{itemize}
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*}
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text*[exo1 :: Exercise,
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concerns= "{setter,student,checker,externalExaminer}"]
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{* On considère la fonction h définie sur l’intervalle [0..+\<infinity>] par :
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@{term "h(x) = x * exponent (-x)"}
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*}
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definition h :: "real \<Rightarrow> real"
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where "h x \<equiv> x * exp (- x)"
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text*[q1::Task, concerns= "{setter,student}",
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level="oneStar", mark="1::int", type="formal"]
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{* Déterminer la limite de la fonction @{term h} en +\<infinity>. *}
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text*[a1::Answer_Formal_Step] {* Fill in term and justification*}
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lemma q1 : "(h \<longlongrightarrow> (0::real)) at_top" sorry
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text*[v1::Validation, proofs="[@{thm ''HOL.refl''}::thm]"] {* See lemma @{thm q1}. *}
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text*[q2::Task, concerns= "{setter,checker,student}",
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level="oneStar", mark="1::int", type="formal"]
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{* Étudier les variations de la fonction @{term h} sur l'intervalle [0..+\<infinity>] et
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dresser son tableau de variation *}
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text*[a2::Answer_Formal_Step]
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{* Fill in term and justification*}
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definition h' :: "real \<Rightarrow> real"
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where "h' x \<equiv> (1 - x) * exp (- x)"
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lemma q2_a : "DERIV h x :> h' x"
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proof -
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have * : "DERIV (exp \<circ> uminus) x :> - (exp (-x))"
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sorry (* by (simp add: has_derivative_compose) *)
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have ** : "DERIV id x :> 1"
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by (metis DERIV_ident eq_id_iff)
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have *** : "DERIV h x :> x * (- (exp (- x))) + 1 * (exp (- x))"
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sorry (* by (simp add: * ** has_derivative_mult comp_def) *)
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show ?thesis
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sorry (* by (metis "***" left_diff_distrib mult_minus_right uminus_add_conv_diff) *)
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qed
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lemma q2_b : "0 \<le> x \<and> x \<le> y \<and> y \<le> 1 \<Longrightarrow> h x \<le> h y"
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sorry
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lemma q2_c : "1 \<le> x \<and> x \<le> y \<Longrightarrow> h x \<ge> h y"
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sorry
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text*[v2::Validation, proofs="[@{thm ''BAC2017.q2_b''}, @{thm ''BAC2017.q2_c''}]"]
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{* See lemmas @{thm q2_b} and @{thm q2_c}. *}
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text*[q3a::Task, concerns= "{setter,checker,student}",
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level="oneStar", mark="1::int", type="formal"]
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{* Vérifier que pour tout nombre réel x appartenant à l'intervalle [0..+\<infinity>], on a :
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@{term "h x = (exp (- x)) - (h' x)"}. *}
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text*[a3a::Answer_Formal_Step]
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{* Fill in term and justification*}
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lemma q3a : "h x = (exp (- x)) - (h' x)"
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by (simp add : h_def h'_def left_diff_distrib)
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subsubsection*[v3a::Validation, proofs="[@{thm ''BAC2017.q3a''}::thm]"]
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{* See lemma @{thm q3a}. *}
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subsection*[sol1 :: Solution,
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content="[exo1::Exercise]",
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valids = "[v1::Validation,v2,v3a]"]
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{* See validations. *}
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close_monitor*[exam]
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end
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@ -1,11 +0,0 @@
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session "BAC2017" = "Isabelle_DOF" +
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options [document = pdf, document_output = "output",quick_and_dirty=true]
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theories [document = false]
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"Deriv"
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"Transcendental"
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theories
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BAC2017
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document_files
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"isadof.cfg"
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"preamble.tex"
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"build"
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@ -1,46 +0,0 @@
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#!/usr/bin/env bash
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# Copyright (c) 2018-2019 The University of Sheffield. All rights reserved.
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# 2018 The University of Paris-Sud. All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions
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# are met:
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# 1. Redistributions of source code must retain the above copyright
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# notice, this list of conditions and the following disclaimer.
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# 2. Redistributions in binary form must reproduce the above copyright
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# notice, this list of conditions and the following disclaimer in
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# the documentation and/or other materials provided with the
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# distribution.
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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# POSSIBILITY OF SUCH DAMAGE.
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#
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# SPDX-License-Identifier: BSD-2-Clause
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set -e
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if [ ! -f $ISABELLE_HOME_USER/DOF/document-template/build_lib.sh ]; then
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echo ""
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echo "Error: Isabelle/DOF not installed"
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echo "====="
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echo "This is a Isabelle/DOF project. The document preparation requires"
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echo "the Isabelle/DOF framework. Please obtain the framework by cloning"
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echo "the Isabelle/DOF git repository, i.e.: "
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echo " git clone https://git.logicalhacking.com/HOL-OCL/Isabelle_DOF"
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echo "You can install the framework as follows:"
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echo " cd Isabelle_DOF/document-generator"
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echo " ./install"
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echo ""
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exit 1
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fi
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cp $ISABELLE_HOME_USER/DOF/document-template/build_lib.sh .
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source build_lib.sh
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@ -1,2 +0,0 @@
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Template: scrartcl
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Ontology: mathex
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@ -1,47 +0,0 @@
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%% Copyright (C) 2018 The University of Sheffield
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%% 2018 The University of Paris-Sud
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%%
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%% License:
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%% This program can be redistributed and/or modified under the terms
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%% of the LaTeX Project Public License Distributed from CTAN
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%% archives in directory macros/latex/base/lppl.txt; either
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%% version 1 of the License, or any later version.
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%% OR
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%% The 2-clause BSD-style license.
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%%
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%% SPDX-License-Identifier: LPPL-1.0+ OR BSD-2-Clause
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%% This is a placeholder for user-specific configuration and packages.
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\title{<TITLE>}
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\author{<AUTHOR>}
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\newkeycommand\isaDofTextExercise[label=,type=,Exercise.content=,content=,concerns=,][1]{%
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\begin{Exercise}
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#1
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\end{Exercise}
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}
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\newkeycommand\isaDofTextSolution[Task.concerns=,concerns=,content=,valids=,][1]{%
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#1
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}
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\newkeycommand\isaDofSectionSolution[Task.concerns=,concerns=,content=,valids=,][1]{%
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#1
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}
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\newkeycommand\isaDofSubsectionSolution[Task.concerns=,concerns=,content=,valids=,][1]{%
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#1
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}
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\newkeycommand\isaDofSubsubsectionSolution[Task.concerns=,concerns=,content=,valids=,][1]{%
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#1
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}
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\newkeycommand\isaDofTextExercise[Task.concerns=,concerns=,content=,][1]{%
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#1
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}
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\newkeycommand\isaDofTextValidation[tests=,proofs=,][1]{%
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#1
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}
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