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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E32">Def13</font></span>   defines <a href="ltlaxio4.html#M4" title="LTLAXIO4:mode.4">path</a> <a onclick="hs(this)" href="javascript:()">LTLAXIO4:def 13 : <br/></a><span> for <font color="Olive" title="b1">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><br/>  for <font color="Olive" title="b2">T</font> being    <a href="ltlaxio4.html#M3" title="LTLAXIO4:mode.3">pnptree</a> of <font color="Olive" title="b1">P</font><br/>  for <font color="Olive">b<sub>3</sub></font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">T</font></span>)</span> holds <br/> ( <font color="Olive">b<sub>3</sub></font> is    <a href="ltlaxio4.html#M4" title="LTLAXIO4:mode.4">path</a> of <font color="Olive" title="b2">T</font> iff ( <font color="Olive">b<sub>3</sub></font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; (  for <font color="Olive" title="b4">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive">b<sub>3</sub></font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="trees_2.html#K1" title="TREES_2:func.1">succ</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">k</font></span>)</span> ) ) );<br/></span></div>
