lambda-sub/graphs/dependency.svg

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<text text-anchor="start" x="406.48" y="-2591.4" font-family="Inter" font-weight="bold" font-size="12.00">Milner&#39;s Lambda&#45;Calculus with Partial Substitutions &#45; theorem dependency (M4)</text>
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<title>open_rec_occurs_false&#45;&gt;open_rec_zplug_lift</title>
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<title>open_rec_occurs_false&#45;&gt;full_comp_aux</title>
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<!-- open_rec_occurs_false&#45;&gt;subst_notin -->
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<title>open_rec_occurs_false&#45;&gt;subst_notin</title>
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<!-- open_rec_occurs_false&#45;&gt;full_comp_aux_sub -->
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<title>open_rec_occurs_false&#45;&gt;full_comp_aux_sub</title>
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<title>close_rec_notin&#45;&gt;subst_notin</title>
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<title>close_rec_fvs&#45;&gt;subst_fvs</title>
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<g id="edge4" class="edge">
<title>open_rec_bvar_neq&#45;&gt;open_rec_fvs</title>
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<!-- open_rec_fvs&#45;&gt;subst_fvs -->
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<title>open_rec_fvs&#45;&gt;subst_fvs</title>
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<title>subst_lc_self</title>
<g id="a_node85"><a xlink:title="subst_lc_self theory/Substitution.v https://arxiv.org/html/2312.13270v1">
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<!-- subst_fvar_self&#45;&gt;subst_lc_self -->
<g id="edge63" class="edge">
<title>subst_fvar_self&#45;&gt;subst_lc_self</title>
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<title>subst_fvar_other</title>
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<title>subst_fvar_other&#45;&gt;subst_other</title>
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<g id="node100" class="node">
<title>star_red_sub_full_comp</title>
<g id="a_node100"><a xlink:title="star_red_sub_full_comp theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="752.81" cy="-281" rx="65.64" ry="18"/>
<text text-anchor="middle" x="752.81" y="-278.8" font-family="Inter" font-size="9.00" fill="#222222">star_red_sub_full_comp</text>
</a>
</g>
</g>
<!-- Plus_to_Star&#45;&gt;star_red_sub_full_comp -->
<g id="edge79" class="edge">
<title>Plus_to_Star&#45;&gt;star_red_sub_full_comp</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M615.34,-301.49C636.57,-298.3 663.88,-294.2 688.49,-290.51"/>
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<!-- Star_red1_context -->
<g id="node18" class="node">
<title>Star_red1_context</title>
<g id="a_node18"><a xlink:title="Star_red1_context theory/Closure.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="65.24" y="-1306.8" font-family="Inter" font-size="9.00" fill="#222222">Star_red1_context</text>
</a>
</g>
</g>
<!-- star_one_trans -->
<g id="node19" class="node">
<title>star_one_trans</title>
<g id="a_node19"><a xlink:title="star_one_trans theory/Closure.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1361" rx="45.07" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1358.8" font-family="Inter" font-size="9.00" fill="#222222">star_one_trans</text>
</a>
</g>
</g>
<!-- in_comb -->
<g id="node20" class="node">
<title>in_comb</title>
<g id="a_node20"><a xlink:title="in_comb theory/Enumerate.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1465" rx="30.04" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1462.8" font-family="Inter" font-size="9.00" fill="#222222">in_comb</text>
</a>
</g>
</g>
<!-- size_all_terms -->
<g id="node22" class="node">
<title>size_all_terms</title>
<g id="a_node22"><a xlink:title="size_all_terms theory/Enumerate.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-1439" rx="43.1" ry="18"/>
<text text-anchor="middle" x="239.88" y="-1436.8" font-family="Inter" font-size="9.00" fill="#222222">size_all_terms</text>
</a>
</g>
</g>
<!-- in_comb&#45;&gt;size_all_terms -->
<g id="edge9" class="edge">
<title>in_comb&#45;&gt;size_all_terms</title>
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<!-- pow2_pos -->
<g id="node21" class="node">
<title>pow2_pos</title>
<g id="a_node21"><a xlink:title="pow2_pos theory/Enumerate.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1413" rx="34.13" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1410.8" font-family="Inter" font-size="9.00" fill="#222222">pow2_pos</text>
</a>
</g>
</g>
<!-- pow2_pos&#45;&gt;size_all_terms -->
<g id="edge10" class="edge">
<title>pow2_pos&#45;&gt;size_all_terms</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M98.31,-1417.83C124.8,-1421.82 162.75,-1427.54 192.55,-1432.02"/>
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<!-- enumerate_check -->
<g id="node23" class="node">
<title>enumerate_check</title>
<g id="a_node23"><a xlink:title="enumerate_check theory/Enumerate.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="1232.27" cy="-741" rx="53.89" ry="18"/>
<text text-anchor="middle" x="1232.27" y="-738.8" font-family="Inter" font-size="9.00" fill="#222222">enumerate_check</text>
</a>
</g>
</g>
<!-- enumerate_sound -->
<g id="node24" class="node">
<title>enumerate_sound</title>
<g id="a_node24"><a xlink:title="enumerate_sound theory/Enumerate.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="752.81" cy="-711" rx="53.23" ry="18"/>
<text text-anchor="middle" x="752.81" y="-708.8" font-family="Inter" font-size="9.00" fill="#222222">enumerate_sound</text>
</a>
</g>
</g>
<!-- enumerate_complete -->
<g id="node25" class="node">
<title>enumerate_complete</title>
<g id="a_node25"><a xlink:title="enumerate_complete theory/Enumerate.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="752.81" cy="-521" rx="61.55" ry="18"/>
<text text-anchor="middle" x="752.81" y="-518.8" font-family="Inter" font-size="9.00" fill="#222222">enumerate_complete</text>
</a>
</g>
</g>
<!-- Plus_red1_context -->
<g id="node26" class="node">
<title>Plus_red1_context</title>
<g id="a_node26"><a xlink:title="Plus_red1_context theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="577.6" cy="-411" rx="53.23" ry="18"/>
<text text-anchor="middle" x="577.6" y="-408.8" font-family="Inter" font-size="9.00" fill="#222222">Plus_red1_context</text>
</a>
</g>
</g>
<!-- lemma_2_3_beta_sim -->
<g id="node41" class="node">
<title>lemma_2_3_beta_sim</title>
<g id="a_node41"><a xlink:title="lemma_2_3_beta_sim (section 2.3) theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="752.81" y="-382.8" font-family="Inter" font-size="9.00" fill="#222222">lemma_2_3_beta_sim</text>
</a>
</g>
</g>
<!-- Plus_red1_context&#45;&gt;lemma_2_3_beta_sim -->
<g id="edge31" class="edge">
<title>Plus_red1_context&#45;&gt;lemma_2_3_beta_sim</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M626.39,-403.83C647.17,-400.71 671.7,-397.02 693.54,-393.75"/>
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<!-- occurs_count_zero -->
<g id="node27" class="node">
<title>occurs_count_zero</title>
<g id="a_node27"><a xlink:title="occurs_count_zero theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-208" rx="54.7" ry="18"/>
<text text-anchor="middle" x="239.88" y="-205.8" font-family="Inter" font-size="9.00" fill="#222222">occurs_count_zero</text>
</a>
</g>
</g>
<!-- occurs_count_pos -->
<g id="node29" class="node">
<title>occurs_count_pos</title>
<g id="a_node29"><a xlink:title="occurs_count_pos theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="408.74" cy="-205" rx="53.89" ry="18"/>
<text text-anchor="middle" x="408.74" y="-202.8" font-family="Inter" font-size="9.00" fill="#222222">occurs_count_pos</text>
</a>
</g>
</g>
<!-- occurs_count_zero&#45;&gt;occurs_count_pos -->
<g id="edge14" class="edge">
<title>occurs_count_zero&#45;&gt;occurs_count_pos</title>
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<!-- occurs_count_zero&#45;&gt;full_comp_aux -->
<g id="edge19" class="edge">
<title>occurs_count_zero&#45;&gt;full_comp_aux</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M280.55,-220.13C289.46,-223.82 298.55,-228.42 306.27,-234 311.41,-237.71 362.06,-299.19 389.8,-333.05"/>
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<!-- occurs_count_zero&#45;&gt;full_comp_aux_sub -->
<g id="edge70" class="edge">
<title>occurs_count_zero&#45;&gt;full_comp_aux_sub</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M281.27,-219.86C305.38,-226.94 336.09,-235.96 361.21,-243.34"/>
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<!-- occurs_count_false -->
<g id="node28" class="node">
<title>occurs_count_false</title>
<g id="a_node28"><a xlink:title="occurs_count_false theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-398" rx="56.66" ry="18"/>
<text text-anchor="middle" x="65.24" y="-395.8" font-family="Inter" font-size="9.00" fill="#222222">occurs_count_false</text>
</a>
</g>
</g>
<!-- occurs_count_zfill_plug -->
<g id="node32" class="node">
<title>occurs_count_zfill_plug</title>
<g id="a_node32"><a xlink:title="occurs_count_zfill_plug theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-398" rx="66.29" ry="18"/>
<text text-anchor="middle" x="239.88" y="-395.8" font-family="Inter" font-size="9.00" fill="#222222">occurs_count_zfill_plug</text>
</a>
</g>
</g>
<!-- occurs_count_false&#45;&gt;occurs_count_zfill_plug -->
<g id="edge15" class="edge">
<title>occurs_count_false&#45;&gt;occurs_count_zfill_plug</title>
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<!-- occurs_lift_self -->
<g id="node30" class="node">
<title>occurs_lift_self</title>
<g id="a_node30"><a xlink:title="occurs_lift_self theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-303" rx="46.38" ry="18"/>
<text text-anchor="middle" x="65.24" y="-300.8" font-family="Inter" font-size="9.00" fill="#222222">occurs_lift_self</text>
</a>
</g>
</g>
<!-- occurs_lift_self&#45;&gt;occurs_count_zfill_plug -->
<g id="edge16" class="edge">
<title>occurs_lift_self&#45;&gt;occurs_count_zfill_plug</title>
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<!-- occurs_lift_self&#45;&gt;open_rec_zplug_lift -->
<g id="edge17" class="edge">
<title>occurs_lift_self&#45;&gt;open_rec_zplug_lift</title>
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<!-- zdecs_nonempty -->
<g id="node31" class="node">
<title>zdecs_nonempty</title>
<g id="a_node31"><a xlink:title="zdecs_nonempty theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-312" rx="51.27" ry="18"/>
<text text-anchor="middle" x="239.88" y="-309.8" font-family="Inter" font-size="9.00" fill="#222222">zdecs_nonempty</text>
</a>
</g>
</g>
<!-- zdecs_nonempty&#45;&gt;full_comp_aux -->
<g id="edge23" class="edge">
<title>zdecs_nonempty&#45;&gt;full_comp_aux</title>
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<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="364.42,-346.01 370.76,-345.47 365.47,-341.94 364.42,-346.01"/>
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<!-- zdecs_nonempty&#45;&gt;full_comp_aux_sub -->
<g id="edge76" class="edge">
<title>zdecs_nonempty&#45;&gt;full_comp_aux_sub</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M277.91,-299.79C303.17,-291.47 336.75,-280.4 363.43,-271.6"/>
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<!-- occurs_count_zfill_plug&#45;&gt;full_comp_aux -->
<g id="edge20" class="edge">
<title>occurs_count_zfill_plug&#45;&gt;full_comp_aux</title>
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<!-- occurs_count_zfill_plug&#45;&gt;full_comp_aux_sub -->
<g id="edge71" class="edge">
<title>occurs_count_zfill_plug&#45;&gt;full_comp_aux_sub</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M261.34,-380.71C292.11,-354.71 350.21,-305.61 383.21,-277.73"/>
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<!-- open_rec_zplug_lift&#45;&gt;full_comp_aux -->
<g id="edge22" class="edge">
<title>open_rec_zplug_lift&#45;&gt;full_comp_aux</title>
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<!-- open_rec_zplug_lift&#45;&gt;full_comp_aux_sub -->
<g id="edge73" class="edge">
<title>open_rec_zplug_lift&#45;&gt;full_comp_aux_sub</title>
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<g id="node35" class="node">
<title>lemma_2_2_full_comp</title>
<g id="a_node35"><a xlink:title="lemma_2_2_full_comp (section 2.2) theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
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</a>
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<!-- full_comp_aux&#45;&gt;lemma_2_2_full_comp -->
<g id="edge25" class="edge">
<title>full_comp_aux&#45;&gt;lemma_2_2_full_comp</title>
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<!-- lemma_2_2_full_comp&#45;&gt;lemma_2_3_beta_sim -->
<g id="edge32" class="edge">
<title>lemma_2_2_full_comp&#45;&gt;lemma_2_3_beta_sim</title>
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<!-- red1_root_fv -->
<g id="node38" class="node">
<title>red1_root_fv</title>
<g id="a_node38"><a xlink:title="red1_root_fv theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="408.74" y="-890.8" font-family="Inter" font-size="9.00" fill="#222222">red1_root_fv</text>
</a>
</g>
</g>
<!-- fvs_zplug_lift&#45;&gt;red1_root_fv -->
<g id="edge27" class="edge">
<title>fvs_zplug_lift&#45;&gt;red1_root_fv</title>
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<!-- plug_fv_mono -->
<g id="node37" class="node">
<title>plug_fv_mono</title>
<g id="a_node37"><a xlink:title="plug_fv_mono theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="408.74" cy="-945" rx="42.95" ry="18"/>
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</a>
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<!-- red1r_fv -->
<g id="node39" class="node">
<title>red1r_fv</title>
<g id="a_node39"><a xlink:title="red1r_fv theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="577.6" cy="-919" rx="28.74" ry="18"/>
<text text-anchor="middle" x="577.6" y="-916.8" font-family="Inter" font-size="9.00" fill="#222222">red1r_fv</text>
</a>
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<!-- plug_fv_mono&#45;&gt;red1r_fv -->
<g id="edge28" class="edge">
<title>plug_fv_mono&#45;&gt;red1r_fv</title>
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<!-- red1_root_fv&#45;&gt;red1r_fv -->
<g id="edge29" class="edge">
<title>red1_root_fv&#45;&gt;red1r_fv</title>
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<g id="node40" class="node">
<title>lemma_2_1_fv_preserved</title>
<g id="a_node40"><a xlink:title="lemma_2_1_fv_preserved (section 2.1) theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
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</a>
</g>
</g>
<!-- red1r_fv&#45;&gt;lemma_2_1_fv_preserved -->
<g id="edge30" class="edge">
<title>red1r_fv&#45;&gt;lemma_2_1_fv_preserved</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M606.82,-919C628.38,-919 659,-919 686.54,-919"/>
<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="686.73,-921.1 692.73,-919 686.73,-916.9 686.73,-921.1"/>
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<!-- gen_fv_preserved -->
<g id="node55" class="node">
<title>gen_fv_preserved</title>
<g id="a_node55"><a xlink:title="gen_fv_preserved theory/Random.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="921.68" cy="-830" rx="52.58" ry="18"/>
<text text-anchor="middle" x="921.68" y="-827.8" font-family="Inter" font-size="9.00" fill="#222222">gen_fv_preserved</text>
</a>
</g>
</g>
<!-- lemma_2_1_fv_preserved&#45;&gt;gen_fv_preserved -->
<g id="edge40" class="edge">
<title>lemma_2_1_fv_preserved&#45;&gt;gen_fv_preserved</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M801.67,-900.89C807.45,-898.39 813.22,-895.73 818.63,-893 844.23,-880.09 871.81,-862.84 891.84,-849.65"/>
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<!-- corpus_fv_preserved -->
<g id="node108" class="node">
<title>corpus_fv_preserved</title>
<g id="a_node108"><a xlink:title="corpus_fv_preserved theory/Tests.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="921.68" y="-897.8" font-family="Inter" font-size="9.00" fill="#222222">corpus_fv_preserved</text>
</a>
</g>
</g>
<!-- lemma_2_1_fv_preserved&#45;&gt;corpus_fv_preserved -->
<g id="edge87" class="edge">
<title>lemma_2_1_fv_preserved&#45;&gt;corpus_fv_preserved</title>
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<!-- Plus_trans -->
<g id="node42" class="node">
<title>Plus_trans</title>
<g id="a_node42"><a xlink:title="Plus_trans theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1517" rx="34.78" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1514.8" font-family="Inter" font-size="9.00" fill="#222222">Plus_trans</text>
</a>
</g>
</g>
<!-- Plus_step_trans -->
<g id="node43" class="node">
<title>Plus_step_trans</title>
<g id="a_node43"><a xlink:title="Plus_step_trans theory/Metatheory.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1569" rx="47.19" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1566.8" font-family="Inter" font-size="9.00" fill="#222222">Plus_step_trans</text>
</a>
</g>
</g>
<!-- par_red1_iff -->
<g id="node44" class="node">
<title>par_red1_iff</title>
<g id="a_node44"><a xlink:title="par_red1_iff theory/Parallel.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1621" rx="37.56" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1618.8" font-family="Inter" font-size="9.00" fill="#222222">par_red1_iff</text>
</a>
</g>
</g>
<!-- par_to_red1_or_eq -->
<g id="node47" class="node">
<title>par_to_red1_or_eq</title>
<g id="a_node47"><a xlink:title="par_to_red1_or_eq theory/Parallel.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-1647" rx="53.23" ry="18"/>
<text text-anchor="middle" x="239.88" y="-1644.8" font-family="Inter" font-size="9.00" fill="#222222">par_to_red1_or_eq</text>
</a>
</g>
</g>
<!-- par_red1_iff&#45;&gt;par_to_red1_or_eq -->
<g id="edge33" class="edge">
<title>par_red1_iff&#45;&gt;par_to_red1_or_eq</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M101.18,-1626.26C125.17,-1629.88 157.5,-1634.74 184.81,-1638.86"/>
<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="184.66,-1640.96 190.91,-1639.78 185.29,-1636.81 184.66,-1640.96"/>
</g>
<!-- red1_or_eq_to_par -->
<g id="node48" class="node">
<title>red1_or_eq_to_par</title>
<g id="a_node48"><a xlink:title="red1_or_eq_to_par theory/Parallel.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-1595" rx="53.23" ry="18"/>
<text text-anchor="middle" x="239.88" y="-1592.8" font-family="Inter" font-size="9.00" fill="#222222">red1_or_eq_to_par</text>
</a>
</g>
</g>
<!-- par_red1_iff&#45;&gt;red1_or_eq_to_par -->
<g id="edge34" class="edge">
<title>par_red1_iff&#45;&gt;red1_or_eq_to_par</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M101.18,-1615.74C125.17,-1612.12 157.5,-1607.26 184.81,-1603.14"/>
<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="185.29,-1605.19 190.91,-1602.22 184.66,-1601.04 185.29,-1605.19"/>
</g>
<!-- red1_in_par -->
<g id="node45" class="node">
<title>red1_in_par</title>
<g id="a_node45"><a xlink:title="red1_in_par theory/Parallel.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1673" rx="37.56" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1670.8" font-family="Inter" font-size="9.00" fill="#222222">red1_in_par</text>
</a>
</g>
</g>
<!-- par_context -->
<g id="node46" class="node">
<title>par_context</title>
<g id="a_node46"><a xlink:title="par_context theory/Parallel.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1725" rx="38.87" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1722.8" font-family="Inter" font-size="9.00" fill="#222222">par_context</text>
</a>
</g>
</g>
<!-- par_reflexive -->
<g id="node49" class="node">
<title>par_reflexive</title>
<g id="a_node49"><a xlink:title="par_reflexive theory/Parallel.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1777" rx="41.64" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1774.8" font-family="Inter" font-size="9.00" fill="#222222">par_reflexive</text>
</a>
</g>
</g>
<!-- gen_list_length -->
<g id="node50" class="node">
<title>gen_list_length</title>
<g id="a_node50"><a xlink:title="gen_list_length theory/Random.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1829" rx="46.38" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1826.8" font-family="Inter" font-size="9.00" fill="#222222">gen_list_length</text>
</a>
</g>
</g>
<!-- check_term_true -->
<g id="node51" class="node">
<title>check_term_true</title>
<g id="a_node51"><a xlink:title="check_term_true theory/Random.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="921.68" cy="-741" rx="50.61" ry="18"/>
<text text-anchor="middle" x="921.68" y="-738.8" font-family="Inter" font-size="9.00" fill="#222222">check_term_true</text>
</a>
</g>
</g>
<!-- check_all_true -->
<g id="node52" class="node">
<title>check_all_true</title>
<g id="a_node52"><a xlink:title="check_all_true theory/Random.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="1080.15" cy="-741" rx="44.41" ry="18"/>
<text text-anchor="middle" x="1080.15" y="-738.8" font-family="Inter" font-size="9.00" fill="#222222">check_all_true</text>
</a>
</g>
</g>
<!-- check_term_true&#45;&gt;check_all_true -->
<g id="edge37" class="edge">
<title>check_term_true&#45;&gt;check_all_true</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M972.62,-741C990.78,-741 1011.29,-741 1029.43,-741"/>
<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="1029.48,-743.1 1035.48,-741 1029.48,-738.9 1029.48,-743.1"/>
</g>
<!-- check_all_true&#45;&gt;enumerate_check -->
<g id="edge11" class="edge">
<title>check_all_true&#45;&gt;enumerate_check</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M1124.97,-741C1139.72,-741 1156.42,-741 1172.14,-741"/>
<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="1172.35,-743.1 1178.35,-741 1172.35,-738.9 1172.35,-743.1"/>
</g>
<!-- gen_sound -->
<g id="node53" class="node">
<title>gen_sound</title>
<g id="a_node53"><a xlink:title="gen_sound theory/Random.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="752.81" cy="-867" rx="35.59" ry="18"/>
<text text-anchor="middle" x="752.81" y="-864.8" font-family="Inter" font-size="9.00" fill="#222222">gen_sound</text>
</a>
</g>
</g>
<!-- gen_complete -->
<g id="node54" class="node">
<title>gen_complete</title>
<g id="a_node54"><a xlink:title="gen_complete theory/Random.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="752.81" cy="-469" rx="43.76" ry="18"/>
<text text-anchor="middle" x="752.81" y="-466.8" font-family="Inter" font-size="9.00" fill="#222222">gen_complete</text>
</a>
</g>
</g>
<!-- zdecs_sound -->
<g id="node56" class="node">
<title>zdecs_sound</title>
<g id="a_node56"><a xlink:title="zdecs_sound theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-450" rx="40.98" ry="18"/>
<text text-anchor="middle" x="239.88" y="-447.8" font-family="Inter" font-size="9.00" fill="#222222">zdecs_sound</text>
</a>
</g>
</g>
<!-- zdecs_sound&#45;&gt;full_comp_aux -->
<g id="edge24" class="edge">
<title>zdecs_sound&#45;&gt;full_comp_aux</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M272.44,-439.05C283.39,-434.84 295.59,-429.67 306.27,-424 333.51,-409.55 362.38,-389.38 382.33,-374.58"/>
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</g>
<!-- root_steps_sound -->
<g id="node59" class="node">
<title>root_steps_sound</title>
<g id="a_node59"><a xlink:title="root_steps_sound theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="408.74" cy="-729" rx="51.27" ry="18"/>
<text text-anchor="middle" x="408.74" y="-726.8" font-family="Inter" font-size="9.00" fill="#222222">root_steps_sound</text>
</a>
</g>
</g>
<!-- zdecs_sound&#45;&gt;root_steps_sound -->
<g id="edge42" class="edge">
<title>zdecs_sound&#45;&gt;root_steps_sound</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M277.52,-457.42C288.2,-461.28 298.96,-467.14 306.27,-476 371.62,-555.21 285.52,-622.5 349.27,-703 353,-707.7 357.75,-711.58 362.93,-714.77"/>
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<!-- zdecs_sound&#45;&gt;full_comp_aux_sub -->
<g id="edge77" class="edge">
<title>zdecs_sound&#45;&gt;full_comp_aux_sub</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M276.31,-441.47C286.94,-437.54 297.96,-431.93 306.27,-424 339.8,-392 324.91,-368.43 349.27,-329 360.28,-311.19 375.19,-292.9 387.2,-279.21"/>
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</g>
<!-- zdecs_complete -->
<g id="node57" class="node">
<title>zdecs_complete</title>
<g id="a_node57"><a xlink:title="zdecs_complete theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-677" rx="49.15" ry="18"/>
<text text-anchor="middle" x="239.88" y="-674.8" font-family="Inter" font-size="9.00" fill="#222222">zdecs_complete</text>
</a>
</g>
</g>
<!-- root_steps_complete -->
<g id="node60" class="node">
<title>root_steps_complete</title>
<g id="a_node60"><a xlink:title="root_steps_complete theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="408.74" cy="-677" rx="59.43" ry="18"/>
<text text-anchor="middle" x="408.74" y="-674.8" font-family="Inter" font-size="9.00" fill="#222222">root_steps_complete</text>
</a>
</g>
</g>
<!-- zdecs_complete&#45;&gt;root_steps_complete -->
<g id="edge43" class="edge">
<title>zdecs_complete&#45;&gt;root_steps_complete</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M289.14,-677C306,-677 325.21,-677 343.19,-677"/>
<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="343.23,-679.1 349.23,-677 343.23,-674.9 343.23,-679.1"/>
</g>
<!-- positions_at -->
<g id="node58" class="node">
<title>positions_at</title>
<g id="a_node58"><a xlink:title="positions_at theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="408.74" cy="-781" rx="38.21" ry="18"/>
<text text-anchor="middle" x="408.74" y="-778.8" font-family="Inter" font-size="9.00" fill="#222222">positions_at</text>
</a>
</g>
</g>
<!-- steps_sound -->
<g id="node61" class="node">
<title>steps_sound</title>
<g id="a_node61"><a xlink:title="steps_sound theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="577.6" cy="-763" rx="39.02" ry="18"/>
<text text-anchor="middle" x="577.6" y="-760.8" font-family="Inter" font-size="9.00" fill="#222222">steps_sound</text>
</a>
</g>
</g>
<!-- positions_at&#45;&gt;steps_sound -->
<g id="edge44" class="edge">
<title>positions_at&#45;&gt;steps_sound</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M445.95,-777.09C471.61,-774.33 506.16,-770.6 533.29,-767.67"/>
<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="533.57,-769.75 539.31,-767.02 533.12,-765.58 533.57,-769.75"/>
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<!-- root_steps_sound&#45;&gt;steps_sound -->
<g id="edge45" class="edge">
<title>root_steps_sound&#45;&gt;steps_sound</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M453.58,-737.93C478.86,-743.08 510.45,-749.52 535.29,-754.58"/>
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</g>
<!-- steps_complete -->
<g id="node68" class="node">
<title>steps_complete</title>
<g id="a_node68"><a xlink:title="steps_complete theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="577.6" cy="-573" rx="47.84" ry="18"/>
<text text-anchor="middle" x="577.6" y="-570.8" font-family="Inter" font-size="9.00" fill="#222222">steps_complete</text>
</a>
</g>
</g>
<!-- root_steps_complete&#45;&gt;steps_complete -->
<g id="edge51" class="edge">
<title>root_steps_complete&#45;&gt;steps_complete</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M445.25,-662.61C452.97,-659.1 460.98,-655.15 468.21,-651 498.36,-633.69 530.39,-609.89 551.74,-593.15"/>
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<!-- steps_sound&#45;&gt;enumerate_sound -->
<g id="edge12" class="edge">
<title>steps_sound&#45;&gt;enumerate_sound</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M610.78,-753.34C637.74,-745.25 676.55,-733.6 706.63,-724.56"/>
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</g>
<!-- steps_sound&#45;&gt;gen_sound -->
<g id="edge38" class="edge">
<title>steps_sound&#45;&gt;gen_sound</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M597.63,-778.88C618.56,-795.82 653.68,-822.68 687,-841 696.41,-846.18 707.07,-850.88 716.99,-854.83"/>
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<!-- steps_sound_red1 -->
<g id="node62" class="node">
<title>steps_sound_red1</title>
<g id="a_node62"><a xlink:title="steps_sound_red1 theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="752.81" cy="-763" rx="51.92" ry="18"/>
<text text-anchor="middle" x="752.81" y="-760.8" font-family="Inter" font-size="9.00" fill="#222222">steps_sound_red1</text>
</a>
</g>
</g>
<!-- steps_sound&#45;&gt;steps_sound_red1 -->
<g id="edge46" class="edge">
<title>steps_sound&#45;&gt;steps_sound_red1</title>
<path fill="none" stroke="#9a9a9a" stroke-width="0.8" d="M617.04,-763C639.83,-763 669.15,-763 694.62,-763"/>
<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="694.66,-765.1 700.66,-763 694.66,-760.9 694.66,-765.1"/>
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<!-- has_red_spec -->
<g id="node70" class="node">
<title>has_red_spec</title>
<g id="a_node70"><a xlink:title="has_red_spec theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="752.81" cy="-659" rx="42.95" ry="18"/>
<text text-anchor="middle" x="752.81" y="-656.8" font-family="Inter" font-size="9.00" fill="#222222">has_red_spec</text>
</a>
</g>
</g>
<!-- steps_sound&#45;&gt;has_red_spec -->
<g id="edge55" class="edge">
<title>steps_sound&#45;&gt;has_red_spec</title>
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<!-- corpus_sound -->
<g id="node105" class="node">
<title>corpus_sound</title>
<g id="a_node105"><a xlink:title="corpus_sound theory/Tests.v https://arxiv.org/html/2312.13270v1">
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<!-- steps_sound&#45;&gt;corpus_sound -->
<g id="edge84" class="edge">
<title>steps_sound&#45;&gt;corpus_sound</title>
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<!-- steps_sound_red1&#45;&gt;check_term_true -->
<g id="edge36" class="edge">
<title>steps_sound_red1&#45;&gt;check_term_true</title>
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<!-- steps_sound_red1&#45;&gt;gen_fv_preserved -->
<g id="edge41" class="edge">
<title>steps_sound_red1&#45;&gt;gen_fv_preserved</title>
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<!-- nf_iff_steps_nil -->
<g id="node72" class="node">
<title>nf_iff_steps_nil</title>
<g id="a_node72"><a xlink:title="nf_iff_steps_nil theory/Reduction.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="921.68" y="-634.8" font-family="Inter" font-size="9.00" fill="#222222">nf_iff_steps_nil</text>
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<!-- steps_sound_red1&#45;&gt;nf_iff_steps_nil -->
<g id="edge58" class="edge">
<title>steps_sound_red1&#45;&gt;nf_iff_steps_nil</title>
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<!-- steps_sound_red1&#45;&gt;corpus_fv_preserved -->
<g id="edge88" class="edge">
<title>steps_sound_red1&#45;&gt;corpus_fv_preserved</title>
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<!-- positions_hole -->
<g id="node63" class="node">
<title>positions_hole</title>
<g id="a_node63"><a xlink:title="positions_hole theory/Reduction.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="239.88" y="-499.8" font-family="Inter" font-size="9.00" fill="#222222">positions_hole</text>
</a>
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</g>
<!-- root_steps_in_steps -->
<g id="node64" class="node">
<title>root_steps_in_steps</title>
<g id="a_node64"><a xlink:title="root_steps_in_steps theory/Reduction.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="408.74" y="-466.8" font-family="Inter" font-size="9.00" fill="#222222">root_steps_in_steps</text>
</a>
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</g>
<!-- positions_hole&#45;&gt;root_steps_in_steps -->
<g id="edge47" class="edge">
<title>positions_hole&#45;&gt;root_steps_in_steps</title>
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<!-- root_steps_in_steps&#45;&gt;steps_complete -->
<g id="edge52" class="edge">
<title>root_steps_in_steps&#45;&gt;steps_complete</title>
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<!-- plug_comp -->
<g id="node65" class="node">
<title>plug_comp</title>
<g id="a_node65"><a xlink:title="plug_comp theory/Reduction.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="408.74" y="-622.8" font-family="Inter" font-size="9.00" fill="#222222">plug_comp</text>
</a>
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</g>
<!-- plug_comp&#45;&gt;steps_complete -->
<g id="edge49" class="edge">
<title>plug_comp&#45;&gt;steps_complete</title>
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<!-- positions_comp -->
<g id="node66" class="node">
<title>positions_comp</title>
<g id="a_node66"><a xlink:title="positions_comp theory/Reduction.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="408.74" y="-570.8" font-family="Inter" font-size="9.00" fill="#222222">positions_comp</text>
</a>
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</g>
<!-- positions_comp&#45;&gt;steps_complete -->
<g id="edge50" class="edge">
<title>positions_comp&#45;&gt;steps_complete</title>
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<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="523.5,-575.1 529.5,-573 523.5,-570.9 523.5,-575.1"/>
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<!-- at_ctx_comp -->
<g id="node67" class="node">
<title>at_ctx_comp</title>
<g id="a_node67"><a xlink:title="at_ctx_comp theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="408.74" cy="-521" rx="40.33" ry="18"/>
<text text-anchor="middle" x="408.74" y="-518.8" font-family="Inter" font-size="9.00" fill="#222222">at_ctx_comp</text>
</a>
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</g>
<!-- at_ctx_comp&#45;&gt;steps_complete -->
<g id="edge48" class="edge">
<title>at_ctx_comp&#45;&gt;steps_complete</title>
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<!-- steps_complete&#45;&gt;enumerate_complete -->
<g id="edge13" class="edge">
<title>steps_complete&#45;&gt;enumerate_complete</title>
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<!-- steps_complete&#45;&gt;gen_complete -->
<g id="edge39" class="edge">
<title>steps_complete&#45;&gt;gen_complete</title>
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<!-- steps_complete&#45;&gt;has_red_spec -->
<g id="edge54" class="edge">
<title>steps_complete&#45;&gt;has_red_spec</title>
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<!-- steps_complete&#45;&gt;nf_iff_steps_nil -->
<g id="edge57" class="edge">
<title>steps_complete&#45;&gt;nf_iff_steps_nil</title>
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<!-- corpus_complete -->
<g id="node106" class="node">
<title>corpus_complete</title>
<g id="a_node106"><a xlink:title="corpus_complete theory/Tests.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="752.81" y="-570.8" font-family="Inter" font-size="9.00" fill="#222222">corpus_complete</text>
</a>
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</g>
<!-- steps_complete&#45;&gt;corpus_complete -->
<g id="edge85" class="edge">
<title>steps_complete&#45;&gt;corpus_complete</title>
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<!-- has_red_f -->
<g id="node69" class="node">
<title>has_red_f</title>
<g id="a_node69"><a xlink:title="has_red_f theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="577.6" cy="-659" rx="32.16" ry="18"/>
<text text-anchor="middle" x="577.6" y="-656.8" font-family="Inter" font-size="9.00" fill="#222222">has_red_f</text>
</a>
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</g>
<!-- has_red_f&#45;&gt;has_red_spec -->
<g id="edge53" class="edge">
<title>has_red_f&#45;&gt;has_red_spec</title>
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<polygon fill="#9a9a9a" stroke="#9a9a9a" stroke-width="0.8" points="703.92,-661.1 709.92,-659 703.92,-656.9 703.92,-661.1"/>
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<!-- has_red_spec&#45;&gt;check_term_true -->
<g id="edge35" class="edge">
<title>has_red_spec&#45;&gt;check_term_true</title>
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<!-- red1_dec -->
<g id="node71" class="node">
<title>red1_dec</title>
<g id="a_node71"><a xlink:title="red1_dec theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="921.68" cy="-689" rx="30.7" ry="18"/>
<text text-anchor="middle" x="921.68" y="-686.8" font-family="Inter" font-size="9.00" fill="#222222">red1_dec</text>
</a>
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</g>
<!-- has_red_spec&#45;&gt;red1_dec -->
<g id="edge56" class="edge">
<title>has_red_spec&#45;&gt;red1_dec</title>
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<!-- corpus_decides -->
<g id="node107" class="node">
<title>corpus_decides</title>
<g id="a_node107"><a xlink:title="corpus_decides theory/Tests.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="921.68" y="-582.8" font-family="Inter" font-size="9.00" fill="#222222">corpus_decides</text>
</a>
</g>
</g>
<!-- has_red_spec&#45;&gt;corpus_decides -->
<g id="edge86" class="edge">
<title>has_red_spec&#45;&gt;corpus_decides</title>
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<!-- normal_form_iff_nf -->
<g id="node73" class="node">
<title>normal_form_iff_nf</title>
<g id="a_node73"><a xlink:title="normal_form_iff_nf theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="1080.15" cy="-611" rx="55.35" ry="18"/>
<text text-anchor="middle" x="1080.15" y="-608.8" font-family="Inter" font-size="9.00" fill="#222222">normal_form_iff_nf</text>
</a>
</g>
</g>
<!-- nf_iff_steps_nil&#45;&gt;normal_form_iff_nf -->
<g id="edge59" class="edge">
<title>nf_iff_steps_nil&#45;&gt;normal_form_iff_nf</title>
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<!-- nf_dec -->
<g id="node74" class="node">
<title>nf_dec</title>
<g id="a_node74"><a xlink:title="nf_dec theory/Reduction.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="1080.15" cy="-663" rx="27" ry="18"/>
<text text-anchor="middle" x="1080.15" y="-660.8" font-family="Inter" font-size="9.00" fill="#222222">nf_dec</text>
</a>
</g>
</g>
<!-- nf_iff_steps_nil&#45;&gt;nf_dec -->
<g id="edge60" class="edge">
<title>nf_iff_steps_nil&#45;&gt;nf_dec</title>
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<!-- open_rec_app -->
<g id="node75" class="node">
<title>open_rec_app</title>
<g id="a_node75"><a xlink:title="open_rec_app theory/Substitution.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1881" rx="43.1" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1878.8" font-family="Inter" font-size="9.00" fill="#222222">open_rec_app</text>
</a>
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</g>
<!-- open_rec_lam -->
<g id="node76" class="node">
<title>open_rec_lam</title>
<g id="a_node76"><a xlink:title="open_rec_lam theory/Substitution.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1933" rx="43.76" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1930.8" font-family="Inter" font-size="9.00" fill="#222222">open_rec_lam</text>
</a>
</g>
</g>
<!-- open_rec_esub -->
<g id="node77" class="node">
<title>open_rec_esub</title>
<g id="a_node77"><a xlink:title="open_rec_esub theory/Substitution.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-1985" rx="46.38" ry="18"/>
<text text-anchor="middle" x="65.24" y="-1982.8" font-family="Inter" font-size="9.00" fill="#222222">open_rec_esub</text>
</a>
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</g>
<!-- close_rec_app -->
<g id="node78" class="node">
<title>close_rec_app</title>
<g id="a_node78"><a xlink:title="close_rec_app theory/Substitution.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-2037" rx="44.41" ry="18"/>
<text text-anchor="middle" x="65.24" y="-2034.8" font-family="Inter" font-size="9.00" fill="#222222">close_rec_app</text>
</a>
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</g>
<!-- close_rec_lam -->
<g id="node79" class="node">
<title>close_rec_lam</title>
<g id="a_node79"><a xlink:title="close_rec_lam theory/Substitution.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-2089" rx="44.41" ry="18"/>
<text text-anchor="middle" x="65.24" y="-2086.8" font-family="Inter" font-size="9.00" fill="#222222">close_rec_lam</text>
</a>
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<!-- close_rec_esub -->
<g id="node80" class="node">
<title>close_rec_esub</title>
<g id="a_node80"><a xlink:title="close_rec_esub theory/Substitution.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-2141" rx="46.53" ry="18"/>
<text text-anchor="middle" x="65.24" y="-2138.8" font-family="Inter" font-size="9.00" fill="#222222">close_rec_esub</text>
</a>
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</g>
<!-- subst_app -->
<g id="node81" class="node">
<title>subst_app</title>
<g id="a_node81"><a xlink:title="subst_app theory/Substitution.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-2193" rx="34.13" ry="18"/>
<text text-anchor="middle" x="65.24" y="-2190.8" font-family="Inter" font-size="9.00" fill="#222222">subst_app</text>
</a>
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</g>
<!-- subst_lam -->
<g id="node82" class="node">
<title>subst_lam</title>
<g id="a_node82"><a xlink:title="subst_lam theory/Substitution.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-2245" rx="34.13" ry="18"/>
<text text-anchor="middle" x="65.24" y="-2242.8" font-family="Inter" font-size="9.00" fill="#222222">subst_lam</text>
</a>
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</g>
<!-- subst_esub -->
<g id="node83" class="node">
<title>subst_esub</title>
<g id="a_node83"><a xlink:title="subst_esub theory/Substitution.v https://arxiv.org/html/2312.13270v1">
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<!-- open_rec_lc_atom -->
<g id="node87" class="node">
<title>open_rec_lc_atom</title>
<g id="a_node87"><a xlink:title="open_rec_lc_atom theory/Substitution.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="65.24" y="-2346.8" font-family="Inter" font-size="9.00" fill="#222222">open_rec_lc_atom</text>
</a>
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<!-- open_rec_lc -->
<g id="node88" class="node">
<title>open_rec_lc</title>
<g id="a_node88"><a xlink:title="open_rec_lc theory/Substitution.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="239.88" y="-2346.8" font-family="Inter" font-size="9.00" fill="#222222">open_rec_lc</text>
</a>
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<!-- open_rec_lc_atom&#45;&gt;open_rec_lc -->
<g id="edge65" class="edge">
<title>open_rec_lc_atom&#45;&gt;open_rec_lc</title>
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<!-- red_sub_root_to_red1 -->
<g id="node89" class="node">
<title>red_sub_root_to_red1</title>
<g id="a_node89"><a xlink:title="red_sub_root_to_red1 theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="65.24" y="-2398.8" font-family="Inter" font-size="9.00" fill="#222222">red_sub_root_to_red1</text>
</a>
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<!-- red_sub_to_red1 -->
<g id="node90" class="node">
<title>red_sub_to_red1</title>
<g id="a_node90"><a xlink:title="red_sub_to_red1 theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-2401" rx="47.84" ry="18"/>
<text text-anchor="middle" x="239.88" y="-2398.8" font-family="Inter" font-size="9.00" fill="#222222">red_sub_to_red1</text>
</a>
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</g>
<!-- red_sub_root_to_red1&#45;&gt;red_sub_to_red1 -->
<g id="edge66" class="edge">
<title>red_sub_root_to_red1&#45;&gt;red_sub_to_red1</title>
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<!-- red_sub_context -->
<g id="node91" class="node">
<title>red_sub_context</title>
<g id="a_node91"><a xlink:title="red_sub_context theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="65.24" y="-2450.8" font-family="Inter" font-size="9.00" fill="#222222">red_sub_context</text>
</a>
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</g>
<!-- Star_red_sub_context -->
<g id="node97" class="node">
<title>Star_red_sub_context</title>
<g id="a_node97"><a xlink:title="Star_red_sub_context theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-2453" rx="61.55" ry="18"/>
<text text-anchor="middle" x="239.88" y="-2450.8" font-family="Inter" font-size="9.00" fill="#222222">Star_red_sub_context</text>
</a>
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</g>
<!-- red_sub_context&#45;&gt;Star_red_sub_context -->
<g id="edge69" class="edge">
<title>red_sub_context&#45;&gt;Star_red_sub_context</title>
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<!-- red_sub_gc -->
<g id="node92" class="node">
<title>red_sub_gc</title>
<g id="a_node92"><a xlink:title="red_sub_gc theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-70" rx="36.25" ry="18"/>
<text text-anchor="middle" x="239.88" y="-67.8" font-family="Inter" font-size="9.00" fill="#222222">red_sub_gc</text>
</a>
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</g>
<!-- red_sub_gc&#45;&gt;full_comp_aux_sub -->
<g id="edge74" class="edge">
<title>red_sub_gc&#45;&gt;full_comp_aux_sub</title>
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<!-- red_gc_to_red_sub -->
<g id="node104" class="node">
<title>red_gc_to_red_sub</title>
<g id="a_node104"><a xlink:title="red_gc_to_red_sub theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="408.74" y="-67.8" font-family="Inter" font-size="9.00" fill="#222222">red_gc_to_red_sub</text>
</a>
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</g>
<!-- red_sub_gc&#45;&gt;red_gc_to_red_sub -->
<g id="edge83" class="edge">
<title>red_sub_gc&#45;&gt;red_gc_to_red_sub</title>
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<!-- red_sub_r -->
<g id="node93" class="node">
<title>red_sub_r</title>
<g id="a_node93"><a xlink:title="red_sub_r theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-156" rx="32.82" ry="18"/>
<text text-anchor="middle" x="239.88" y="-153.8" font-family="Inter" font-size="9.00" fill="#222222">red_sub_r</text>
</a>
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</g>
<!-- red_sub_r&#45;&gt;full_comp_aux_sub -->
<g id="edge75" class="edge">
<title>red_sub_r&#45;&gt;full_comp_aux_sub</title>
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<!-- occurs_zfill -->
<g id="node94" class="node">
<title>occurs_zfill</title>
<g id="a_node94"><a xlink:title="occurs_zfill theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-2505" rx="37.56" ry="18"/>
<text text-anchor="middle" x="65.24" y="-2502.8" font-family="Inter" font-size="9.00" fill="#222222">occurs_zfill</text>
</a>
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<!-- zfill_occurs0 -->
<g id="node95" class="node">
<title>zfill_occurs0</title>
<g id="a_node95"><a xlink:title="zfill_occurs0 theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="239.88" cy="-2505" rx="40.98" ry="18"/>
<text text-anchor="middle" x="239.88" y="-2502.8" font-family="Inter" font-size="9.00" fill="#222222">zfill_occurs0</text>
</a>
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</g>
<!-- occurs_zfill&#45;&gt;zfill_occurs0 -->
<g id="edge67" class="edge">
<title>occurs_zfill&#45;&gt;zfill_occurs0</title>
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<!-- R_Gc_disjoint -->
<g id="node96" class="node">
<title>R_Gc_disjoint</title>
<g id="a_node96"><a xlink:title="R_Gc_disjoint theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="408.74" cy="-2505" rx="41.64" ry="18"/>
<text text-anchor="middle" x="408.74" y="-2502.8" font-family="Inter" font-size="9.00" fill="#222222">R_Gc_disjoint</text>
</a>
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</g>
<!-- zfill_occurs0&#45;&gt;R_Gc_disjoint -->
<g id="edge68" class="edge">
<title>zfill_occurs0&#45;&gt;R_Gc_disjoint</title>
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<!-- plus_red_sub_full_comp -->
<g id="node99" class="node">
<title>plus_red_sub_full_comp</title>
<g id="a_node99"><a xlink:title="plus_red_sub_full_comp theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="577.6" y="-252.8" font-family="Inter" font-size="9.00" fill="#222222">plus_red_sub_full_comp</text>
</a>
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</g>
<!-- full_comp_aux_sub&#45;&gt;plus_red_sub_full_comp -->
<g id="edge78" class="edge">
<title>full_comp_aux_sub&#45;&gt;plus_red_sub_full_comp</title>
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<!-- plus_red_sub_full_comp&#45;&gt;star_red_sub_full_comp -->
<g id="edge80" class="edge">
<title>plus_red_sub_full_comp&#45;&gt;star_red_sub_full_comp</title>
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<g id="node101" class="node">
<title>es_count_plug_mono</title>
<g id="a_node101"><a xlink:title="es_count_plug_mono theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
<ellipse fill="#d9ead3" stroke="#38761d" cx="65.24" cy="-2557" rx="60.74" ry="18"/>
<text text-anchor="middle" x="65.24" y="-2554.8" font-family="Inter" font-size="9.00" fill="#222222">es_count_plug_mono</text>
</a>
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<!-- red_gc_measure -->
<g id="node102" class="node">
<title>red_gc_measure</title>
<g id="a_node102"><a xlink:title="red_gc_measure theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="239.88" y="-2554.8" font-family="Inter" font-size="9.00" fill="#222222">red_gc_measure</text>
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<!-- es_count_plug_mono&#45;&gt;red_gc_measure -->
<g id="edge81" class="edge">
<title>es_count_plug_mono&#45;&gt;red_gc_measure</title>
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<!-- red_gc_terminates -->
<g id="node103" class="node">
<title>red_gc_terminates</title>
<g id="a_node103"><a xlink:title="red_gc_terminates theory/Subsystem.v https://arxiv.org/html/2312.13270v1">
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<!-- red_gc_measure&#45;&gt;red_gc_terminates -->
<g id="edge82" class="edge">
<title>red_gc_measure&#45;&gt;red_gc_terminates</title>
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