<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E94">Def61</font></span>   defines <a href="modelc_1.html#K49" title="MODELC_1:func.49">PrePath</a> <a onclick="hs(this)" href="javascript:()">MODELC_1:def 61 : <br/></a><span> for <font color="Olive" title="b1">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">R</font> being   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">s0</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">pai</font> being    <a href="modelc_1.html#M1" title="MODELC_1:mode.1">inf_path</a> of <font color="Olive" title="b2">R</font><br/>  for <font color="Olive" title="b5">n</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( ( <font color="Olive" title="b5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  <a href="modelc_1.html#K49" title="MODELC_1:func.49">PrePath</a> (<font color="Olive" title="b5">n</font>,<font color="Olive" title="b3">s0</font>,<font color="Olive" title="b4">pai</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s0</font> ) &amp; (  not <font color="Olive" title="b5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  <a href="modelc_1.html#K49" title="MODELC_1:func.49">PrePath</a> (<font color="Olive" title="b5">n</font>,<font color="Olive" title="b3">s0</font>,<font color="Olive" title="b4">pai</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">pai</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K2" title="MODELC_1:func.2">k_nat</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_1.html#K2" title="MODELC_1:func.2">k_nat</a> <font color="Olive" title="b5">n</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> ) );<br/></span></div>
