<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: LTLAXIO3:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a> <br/>  for <font color="Olive" title="b2">P</font> being   <a href="ltlaxio3.html#NV3" title="LTLAXIO3:NV.3">consistent</a>  <a href="ltlaxio3.html#NM1" title="LTLAXIO3:NM.1">PNPair</a>  holds <br/>( <font color="Olive" title="b1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ltlaxio3.html#K10" title="LTLAXIO3:func.10">rng</a> <font color="Olive" title="b2">P</font> or <span class="p1"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">P</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span> <a href="ltlaxio3.html#K3" title="LTLAXIO3:func.3">^^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">A</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">P</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span> is  <a href="ltlaxio3.html#NV3" title="LTLAXIO3:NV.3">consistent</a>  or <span class="p1"><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">P</font> <a href="ltlaxio3.html#K8" title="LTLAXIO3:func.8">`1</a></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">P</font> <a href="ltlaxio3.html#K9" title="LTLAXIO3:func.9">`2</a></span>)</span> <a href="ltlaxio3.html#K3" title="LTLAXIO3:func.3">^^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">A</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span><a href="ltlaxio3.html#K11" title="LTLAXIO3:func.11">]</a></span> is  <a href="ltlaxio3.html#NV3" title="LTLAXIO3:NV.3">consistent</a>  )</div></div>
