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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: HILBERT3:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> holds <br/> not <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p3">(<span class="default"><a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Olive" title="b2">b</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p2">(<span class="default"><a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Olive" title="b1">a</font></span>)</span></span>)</span> <a href="hilbert1.html#K3" title="HILBERT1:func.3">=&gt;</a> <span class="p1">(<span class="default"><a href="hilbert2.html#K1" title="HILBERT2:func.1">prop</a> <font color="Olive" title="b1">a</font></span>)</span> is  <a href="hilbert3.html#V2" title="HILBERT3:attr.2">pseudo-canonical</a> </div></div>
