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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E23">Def4</font></span>   defines <a href="jordan_a.html#K2" title="JORDAN_A:func.2">Segm</a> <a onclick="hs(this)" href="javascript:()">JORDAN_A:def 4 : <br/></a><span> for <font color="Olive" title="b1">C</font> being   <a href="topreal2.html#NM1" title="TOPREAL2:NM.1">Simple_closed_curve</a><br/>  for <font color="Olive" title="b2">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">S</font> being    <a href="jordan_a.html#M1" title="JORDAN_A:mode.1">Segmentation</a> of <font color="Olive" title="b1">C</font> holds <br/> ( ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">i</font> &amp; <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">S</font> implies  <a href="jordan_a.html#K2" title="JORDAN_A:func.2">Segm</a> (<font color="Olive" title="b3">S</font>,<font color="Olive" title="b2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">S</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b2">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">S</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Olive" title="b1">C</font>) ) &amp; ( (  not 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">i</font> or  not <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">S</font> ) implies  <a href="jordan_a.html#K2" title="JORDAN_A:func.2">Segm</a> (<font color="Olive" title="b3">S</font>,<font color="Olive" title="b2">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan7.html#K1" title="JORDAN7:func.1">Segment</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">S</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b3">S</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">S</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<font color="Olive" title="b1">C</font>) ) );<br/></span></div>
