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<b>let </b><font color="Maroon">C1</font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>, <font color="Maroon">C2</font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="cohsp_1.html#V8" target="_self">U-continuous</a> <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font>;<br/><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font>;<br/>





<b>set </b><font color="Maroon">X</font> =  <a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font>;<br/>
<a NAME="E1:73"/><i><font color="Green">E26</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C1</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><i><font color="Green">E27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:73_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E2:73_1"/><b>then </b>
 ex <font color="Olive">y</font> being <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a>  ex <font color="Olive">z</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">y</font>,<font color="Olive">z</font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Olive">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">y</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:73_1"/>
<font color="Maroon">x</font> <a href="mcart_1.html#K1">`1</a>  is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:73"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being <a href="finset_1.html#V1">finite</a>  <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font>  st <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">b</font> holds <br/>for <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="txt" href="cohsp_1.html#E3:73"><i><font color="Green">E36</font></i></a>, </i>;<br/>
<a NAME="E4:73"/>
for <font color="Olive">a</font> being <a href="finset_1.html#V1">finite</a>  <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font><br/> for <font color="Olive">y1</font>, <font color="Olive">y2</font> being   <a href="hidden.html#M1">set</a>   st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">y1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">y2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font> holds <br/><span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Olive">y1</font>,<font color="Olive">y2</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T1" target="_self">Th1</a></i>;<br/>
<b>then consider </b><font color="Maroon">g</font> being  <a href="cohsp_1.html#V8" target="_self">U-continuous</a> <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font><b> such that </b><br/><a NAME="E6:73"/><i><font color="Green">E41</font></i>: 
(  <a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">g</font> &amp; ( for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> holds  <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K3" target="_self">Fin</a> <font color="Olive">a</font></span>)</span> ) )
 <b>by </b><i><a class="ref" href="cohsp_1.html#T2" target="_self">Th2</a>, , </i>;<br/>
<a NAME="E7:73"/>
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K3" target="_self">Fin</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:73"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K6" target="_self">graph</a> <font color="Maroon">f</font></span>)</span> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K3" target="_self">Fin</a> <font color="Maroon">a</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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