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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: LTLAXIO2:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">f1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="ltlaxio1.html#NK1" title="LTLAXIO1:NK.1">LTLB_WFF</a>   st  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b1">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b2">f1</font> holds <br/><span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio2.html#K2" title="LTLAXIO2:func.2">con</a> <span class="p4">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <font color="Olive" title="b1">f</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="ltlaxio2.html#K2" title="LTLAXIO2:func.2">con</a> <span class="p5">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <font color="Olive" title="b1">f</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="ltlaxio1.html#K1" title="LTLAXIO1:func.1">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ltlaxio2.html#K2" title="LTLAXIO2:func.2">con</a> <span class="p4">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <font color="Olive" title="b2">f1</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p4">(<span class="default"><a href="ltlaxio2.html#K2" title="LTLAXIO2:func.2">con</a> <span class="p5">(<span class="default"><a href="ltlaxio2.html#K4" title="LTLAXIO2:func.4">nega</a> <font color="Olive" title="b2">f1</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> is  <a href="ltlaxio2.html#NV1" title="LTLAXIO2:NV.1">ctaut</a> </div></div>
