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| <p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∀</mi><mi>i</mi><mo>∈</mo><mrow><mo fence="true">(</mo><mn>0</mn><mo separator="true">,</mo><mrow><mo fence="true">∣</mo><mi>P</mi><mo fence="true">∣</mo></mrow><mo fence="true">]</mo></mrow><mo>:</mo><msub><mi>p</mi><mrow><mi>i</mi><mo>−</mo><mn>1</mn></mrow></msub><mi mathvariant="normal">.</mi><msub><mi>v</mi><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>=</mo><msub><mi>p</mi><mi>i</mi></msub><mi mathvariant="normal">.</mi><msub><mi>v</mi><mrow><mi>o</mi><mi>u</mi><mi>t</mi></mrow></msub><mspace linebreak="newline"></mspace><mi mathvariant="normal">∀</mi><msub><mi>p</mi><mi>i</mi></msub><mo>∈</mo><mi>P</mi><mtext> </mtext><mo>⟹</mo><mtext> </mtext><msub><mi>p</mi><mi>i</mi></msub><mo>∈</mo><mi>E</mi></mrow><annotation encoding="application/x-tex"> | |
| \forall i \in \left(0, \left|P\right|\right]: p_{i-1}.v_{in} = p_i.v_{out} \\ | |
| \forall p_i \in P \implies p_i \in E | |
| </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="mord">∀</span><span class="mord mathdefault">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">∣</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mclose delimcenter" style="top:0em;">∣</span></span><span class="mclose delimcenter" style="top:0em;">]</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.638891em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathdefault">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mord">.</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathdefault">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">.</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">o</span><span class="mord mathdefault mtight">u</span><span class="mord mathdefault mtight">t</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord">∀</span><span class="mord"><span class="mord mathdefault">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.70733em;vertical-align:-0.024em;"></span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">⟹</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.7335400000000001em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathdefault">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span></span></span></span></span></p> | |
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