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<span class="kw">assume </span><a NAME="E1:129_1_1"/>
not  <a href="simplex0.html#K11" title="SIMPLEX0:func.11">subdivision</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c2">KX</font> is  <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:129_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="simplex0.html#K6" title="SIMPLEX0:func.6">degree</a> <font color="Maroon" title="c2">KX</font></span>)</span> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp;  <a href="simplex0.html#K6" title="SIMPLEX0:func.6">degree</a> <span class="p1">(<span class="default"><a href="simplex0.html#K11" title="SIMPLEX0:func.11">subdivision</a> <font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c2">KX</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D12" target="_self" title="SIMPLEX0:def.12">Def12</a>, <a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:129_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#T51" target="_self" title="SIMPLEX0:th.51">Th51</a>, <a class="ref" href="xxreal_0.html#T9" title="XXREAL_0:th.9">XXREAL_0:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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