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<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="chain_1.html#K5" target="_self">cells</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span>) <b>-&gt; </b>   <a href="chain_1.html#M3" target="_self">Cycle</a> of <font color="Maroon">k</font>,<font color="Maroon">G</font> =  <a href="chain_1.html#K15" target="_self">del</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="chain_1.html#K1" target="_self">bool</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" target="_self">cells</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span>, <a href="chain_1.html#K1" target="_self">bool</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" target="_self">cells</a> <font color="Maroon">k</font>,<font color="Maroon">G</font></span>)</span><b> such that </b><br/><a NAME="E2:104_1_1"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">A</font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="chain_1.html#K5" target="_self">cells</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">A</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<a NAME="E3:104_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="chain_1.html#K16" target="_self">Chains</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K1" target="_self">bool</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" target="_self">cells</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="chain_1.html#K16" target="_self">Chains</a> <font color="Maroon">k</font>,<font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K1" target="_self">bool</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" target="_self">cells</a> <font color="Maroon">k</font>,<font color="Maroon">G</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="chain_1.html#K16" target="_self">Chains</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span>,<span class="p1">(<span class="default"><a href="chain_1.html#K16" target="_self">Chains</a> <font color="Maroon">k</font>,<font color="Maroon">G</font></span>)</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="chain_1.html#K16" target="_self">Chains</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="chain_1.html#K16" target="_self">Chains</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">A'</font> = <font color="Maroon">A</font>, <font color="Maroon">B'</font> = <font color="Maroon">B</font> as   <a href="chain_1.html#NM4">Chain</a> of <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font> <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">B</font></span>)</span> = 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">A'</font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Maroon">B'</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="chain_1.html#K15" target="_self">del</a> <span class="p1">(<span class="default"><font color="Maroon">A'</font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Maroon">B'</font></span>)</span>
<b>by </b><i><a class="ref" href="chain_1.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="chain_1.html#K15" target="_self">del</a> <font color="Maroon">A'</font></span>)</span> <a href="chain_1.html#K14" target="_self">+</a> <span class="p1">(<span class="default"><a href="chain_1.html#K15" target="_self">del</a> <font color="Maroon">B'</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="chain_1.html#K15" target="_self">del</a> <font color="Maroon">A'</font></span>)</span> <a href="chain_1.html#K8" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">B'</font></span>)</span>
<b>by </b><i><a class="ref" href="chain_1.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">A'</font></span>)</span> <a href="chain_1.html#K8" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">B'</font></span>)</span>
<b>by </b><i><a class="ref" href="chain_1.html#T7" target="_self">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">f'</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">B</font></span>)</span>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f'</font> as    <a href="mod_4.html#M1">Homomorphism</a> of  <a href="chain_1.html#K16" target="_self">Chains</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font>, <a href="chain_1.html#K16" target="_self">Chains</a> <font color="Maroon">k</font>,<font color="Maroon">G</font> <b>by </b><i><a class="ref" href="mod_4.html#D18">MOD_4:def 18</a></i>;<br/>
<b>take </b>
<font color="Maroon">f'</font>
;<br/>

<b>thus </b><a NAME="E7:104_1_1"/>
for <font color="Olive">A</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="chain_1.html#K16" target="_self">Chains</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font></span>)</span><br/> for <font color="Olive">A'</font> being  <a href="chain_1.html#NM4">Chain</a> of <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">G</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">A'</font> holds <br/><font color="Maroon">f'</font> <a href="funct_2.html#K3">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K15" target="_self">del</a> <font color="Olive">A'</font>
 <b>by </b><i><a class="ref" href="chain_1.html#T7" target="_self">Th7</a></i>;<br/>


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