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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">KX</font> being   <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">P</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds   <a href="simplex0.html#K12" title="SIMPLEX0:func.12">subdivision</a> 1,<font color="Olive" title="b2">P</font>,<font color="Olive" title="b1">KX</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="simplex0.html#K11" title="SIMPLEX0:func.11">subdivision</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b1">KX</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">KX</font> be    <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">P</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds   <a href="simplex0.html#K12" title="SIMPLEX0:func.12">subdivision</a> 1,<font color="Olive" title="b1">P</font>,<font color="Maroon" title="c2">KX</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="simplex0.html#K11" title="SIMPLEX0:func.11">subdivision</a> <font color="Olive" title="b1">P</font>,<font color="Maroon" title="c2">KX</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">P</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="simplex0.html#K12" title="SIMPLEX0:func.12">subdivision</a> 1,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c2">KX</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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><br/>





<span class="kw">consider </span><font color="Maroon" title="c4">F</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><span class="kw"> such that </span><br/><a NAME="E2:141"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">KX</font>
 <span class="kw">and </span><br/><a NAME="E3:141"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="simplex0.html#K12" title="SIMPLEX0:func.12">subdivision</a> 1,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c2">KX</font>
 <span class="kw">and </span><br/><a NAME="E4:141"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">and </span><br/><a NAME="E5:141"/><span class="lab"><font color="Green" title="E59">A3</font></span>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b2">KX1</font> being   <a href="simplex0.html#M1" title="SIMPLEX0:mode.1">SimplicialComplexStr</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b2">KX1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> holds <br/><font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="simplex0.html#K11" title="SIMPLEX0:func.11">subdivision</a> <font color="Maroon" title="c3">P</font>,<font color="Olive" title="b2">KX1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="simplex0.html#D21" target="_self" title="SIMPLEX0:def.21">Def21</a></span>;<br/>
<a NAME="E6:141"/>
<font color="Maroon" title="c4">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:141"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="txt" href="#E5:141"><span class="lab"><font color="Green" title="E59">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:141"/>
 <a href="simplex0.html#K12" title="SIMPLEX0:func.12">subdivision</a> 1,<font color="Maroon" title="c3">P</font>,<font color="Maroon" title="c2">KX</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:141"><span class="lab"><font color="Green" title="E58">A2</font></span></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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