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<b>let </b><font color="Maroon">f</font> be    <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>, <font color="Maroon">g</font> be    <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>;<br/>

<b>assume </b><a NAME="E1:104_1_2"/><i><font color="Green">E51</font></i>: 
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>
 ;<br/>

<b>assume </b><a NAME="E2:104_1_2"/><i><font color="Green">E52</font></i>: 
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">g</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>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1_2_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>;<br/><b>reconsider </b><font color="Maroon">A'</font> = <font color="Maroon">A</font> as   <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> 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/><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">A'</font> = 
 <a href="chain_1.html#K15" target="_self">del</a> <font color="Maroon">A''</font>
<b>by </b><i><a class="ref" href="chain_1.html#T7" target="_self">Th7</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">A'</font>
<b>by </b><i><a class="ref" href="chain_1.html#T8" target="_self">Th8</a></i>
;<br/><b>hence </b><a NAME="E4:104_1_2_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">A</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:104_1_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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