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initial commit: confluence and normalisation

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sneeker committed 2026-09-22 09:20:00 +02:00
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<!-- m3_termination -->
<g id="node10" class="node">
<title>m3_termination</title>
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<text text-anchor="middle" x="954.78" y="-250.14" font-family="Inter" font-size="10.00" fill="#333333">{R,Gc} termination</text>
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<!-- m3_measure&#45;&gt;m3_termination -->
<g id="edge11" class="edge">
<title>m3_measure&#45;&gt;m3_termination</title>
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<!-- m3_termination&#45;&gt;m3_local_confluence -->
<g id="edge12" class="edge">
<title>m3_termination&#45;&gt;m3_local_confluence</title>
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<g id="node12" class="node">
<title>lemma_3_2_sub_nf_unique</title>
<g id="a_node12"><a xlink:title="lemma_3_2_sub_nf_unique (section 3.1) https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="1292.78" y="-250.14" font-family="Inter" font-size="10.00" fill="#333333">Lemma 3.2 sub NF unique</text>
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</g>
<!-- m3_local_confluence&#45;&gt;lemma_3_2_sub_nf_unique -->
<g id="edge14" class="edge">
<title>m3_local_confluence&#45;&gt;lemma_3_2_sub_nf_unique</title>
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<!-- lemma_3_2_sub_nf_unique&#45;&gt;m4_par -->
<g id="edge16" class="edge">
<title>lemma_3_2_sub_nf_unique&#45;&gt;m4_par</title>
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<!-- m5_coherence -->
<g id="node19" class="node">
<title>m5_coherence</title>
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<text text-anchor="middle" x="1628.35" y="-331.14" font-family="Inter" font-size="10.00" fill="#333333">RX + =C coherence</text>
</a>
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<!-- lemma_3_2_sub_nf_unique&#45;&gt;m5_coherence -->
<g id="edge26" class="edge">
<title>lemma_3_2_sub_nf_unique&#45;&gt;m5_coherence</title>
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<!-- m4_par_diamond -->
<g id="node14" class="node">
<title>m4_par_diamond</title>
<g id="a_node14"><a xlink:title="m4_par_diamond (section 3.2) https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="1628.35" y="-220.14" font-family="Inter" font-size="10.00" fill="#333333">par diamond</text>
</a>
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</g>
<!-- m4_par&#45;&gt;m4_par_diamond -->
<g id="edge17" class="edge">
<title>m4_par&#45;&gt;m4_par_diamond</title>
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<!-- m4_par_diamond&#45;&gt;theorem_confluence_terms -->
<g id="edge18" class="edge">
<title>m4_par_diamond&#45;&gt;theorem_confluence_terms</title>
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<!-- theorem_confluence_metaterms -->
<g id="node20" class="node">
<title>theorem_confluence_metaterms</title>
<g id="a_node20"><a xlink:title="theorem_confluence_metaterms (section 3.3) https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="1790.35" y="-331.14" font-family="Inter" font-size="10.00" fill="#333333">Confluence on metaterms</text>
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</g>
<!-- m4_par_diamond&#45;&gt;theorem_confluence_metaterms -->
<g id="edge28" class="edge">
<title>m4_par_diamond&#45;&gt;theorem_confluence_metaterms</title>
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<!-- corollary_6_21_psn -->
<g id="node26" class="node">
<title>corollary_6_21_psn</title>
<g id="a_node26"><a xlink:title="corollary_6_21_psn (section 6) https://arxiv.org/html/2312.13270v1">
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<text text-anchor="middle" x="1936.35" y="-466.14" font-family="Inter" font-size="10.00" fill="#333333">Cor 6.21 PSN</text>
</a>
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</g>
<!-- theorem_confluence_terms&#45;&gt;corollary_6_21_psn -->
<g id="edge35" class="edge">
<title>theorem_confluence_terms&#45;&gt;corollary_6_21_psn</title>
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<!-- m5_mvar&#45;&gt;m5_rx -->
<g id="edge21" class="edge">
<title>m5_mvar&#45;&gt;m5_rx</title>
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<!-- m5_eq_C -->
<g id="node18" class="node">
<title>m5_eq_C</title>
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<text text-anchor="middle" x="1468.07" y="-385.14" font-family="Inter" font-size="10.00" fill="#333333">=C setoid</text>
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</g>
<!-- m5_mvar&#45;&gt;m5_eq_C -->
<g id="edge23" class="edge">
<title>m5_mvar&#45;&gt;m5_eq_C</title>
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<!-- m5_rx&#45;&gt;m5_coherence -->
<g id="edge24" class="edge">
<title>m5_rx&#45;&gt;m5_coherence</title>
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<!-- m5_eq_C&#45;&gt;m5_coherence -->
<g id="edge25" class="edge">
<title>m5_eq_C&#45;&gt;m5_coherence</title>
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<!-- m5_coherence&#45;&gt;theorem_confluence_metaterms -->
<g id="edge27" class="edge">
<title>m5_coherence&#45;&gt;theorem_confluence_metaterms</title>
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<!-- m6_sn -->
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<title>m6_sn</title>
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<text text-anchor="middle" x="1292.78" y="-466.14" font-family="Inter" font-size="10.00" fill="#333333">SN for simply typed</text>
</a>
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</g>
<!-- m6_translation&#45;&gt;m6_sn -->
<g id="edge30" class="edge">
<title>m6_translation&#45;&gt;m6_sn</title>
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<!-- m6_intersection -->
<g id="node23" class="node">
<title>m6_intersection</title>
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<text text-anchor="middle" x="1468.07" y="-466.14" font-family="Inter" font-size="10.00" fill="#333333">intersection typing</text>
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<!-- m6_sn&#45;&gt;m6_intersection -->
<g id="edge31" class="edge">
<title>m6_sn&#45;&gt;m6_intersection</title>
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<!-- m6_typable_sn -->
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<title>m6_typable_sn</title>
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<text text-anchor="middle" x="1628.35" y="-466.14" font-family="Inter" font-size="10.00" fill="#333333">typable → SN</text>
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<!-- m6_intersection&#45;&gt;m6_typable_sn -->
<g id="edge32" class="edge">
<title>m6_intersection&#45;&gt;m6_typable_sn</title>
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<!-- m6_sn_typable -->
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<title>m6_sn_typable</title>
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<text text-anchor="middle" x="1790.35" y="-466.14" font-family="Inter" font-size="10.00" fill="#333333">SN → typable</text>
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<!-- m6_typable_sn&#45;&gt;m6_sn_typable -->
<g id="edge33" class="edge">
<title>m6_typable_sn&#45;&gt;m6_sn_typable</title>
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<!-- m6_sn_typable&#45;&gt;corollary_6_21_psn -->
<g id="edge34" class="edge">
<title>m6_sn_typable&#45;&gt;corollary_6_21_psn</title>
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