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<b>let </b><font color="Maroon">C1</font> be  <a href="rlvect_1.html#V1">strict</a> <a href="vectsp_1.html#NM1">AbGroup</a>, <font color="Maroon">C2</font> be  <a href="rlvect_1.html#V1">strict</a> <a href="vectsp_1.html#NM1">AbGroup</a>;<br/>

<b>assume </b><a NAME="E1:102_1_2"/><i><font color="Green">E54</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C1</font> <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> &amp;  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K12" target="_self">0_</a> <font color="Maroon">k</font>,<font color="Maroon">G</font> &amp; ( for <font color="Olive">A</font>, <font color="Olive">B</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C1</font><br/> for <font color="Olive">A'</font>, <font color="Olive">B'</font> being  <a href="chain_1.html#NM4">Chain</a> of <font color="Maroon">k</font>,<font color="Maroon">G</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">A'</font> &amp; <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">B'</font> holds <br/><font color="Olive">A</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">A'</font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Olive">B'</font> ) &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C2</font> <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> &amp;  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a>  <a href="chain_1.html#K12" target="_self">0_</a> <font color="Maroon">k</font>,<font color="Maroon">G</font> &amp; ( for <font color="Olive">A</font>, <font color="Olive">B</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C2</font><br/> for <font color="Olive">A'</font>, <font color="Olive">B'</font> being  <a href="chain_1.html#NM4">Chain</a> of <font color="Maroon">k</font>,<font color="Maroon">G</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">A'</font> &amp; <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">B'</font> holds <br/><font color="Olive">A</font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Olive">A'</font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Olive">B'</font> ) )
 ;<br/>

<b>set </b><font color="Maroon">X</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K1" target="_self">bool</a> <span class="p3">(<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></span>)</span>,<span class="p2">(<span class="default"><a href="chain_1.html#K1" target="_self">bool</a> <span class="p3">(<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></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<b>reconsider </b><font color="Maroon">op1</font> = the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">C1</font>, <font color="Maroon">op2</font> = the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">C2</font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K1" target="_self">bool</a> <span class="p3">(<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></span>)</span>,<span class="p2">(<span class="default"><a href="chain_1.html#K1" target="_self">bool</a> <span class="p3">(<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></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></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>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="102_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">AB</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K1" target="_self">bool</a> <span class="p3">(<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></span>)</span>,<span class="p2">(<span class="default"><a href="chain_1.html#K1" target="_self">bool</a> <span class="p3">(<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></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/><b>consider </b><font color="Maroon">A'</font> being   <a href="chain_1.html#NM4">Chain</a> of <font color="Maroon">k</font>,<font color="Maroon">G</font>, <font color="Maroon">B'</font> being   <a href="chain_1.html#NM4">Chain</a> of <font color="Maroon">k</font>,<font color="Maroon">G</font><b> such that </b><br/><a NAME="E2:102_1_2_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">AB</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">A'</font>,<font color="Maroon">B'</font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9">DOMAIN_1:9</a></i>;<br/><b>reconsider </b><font color="Maroon">A1</font> = <font color="Maroon">A'</font>, <font color="Maroon">B1</font> = <font color="Maroon">B'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C1</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">A2</font> = <font color="Maroon">A'</font>, <font color="Maroon">B2</font> = <font color="Maroon">B'</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">C2</font> <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">op1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">AB</font> = 
<font color="Maroon">A1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">B1</font>
<b>by </b><i><a class="ref" href="chain_1.html#T7" target="_self">Th7</a></i>
<br/>.= 
<font color="Maroon">A'</font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Maroon">B'</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">A2</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">B2</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">op2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">AB</font>
<b>by </b><i><a class="ref" href="chain_1.html#T7" target="_self">Th7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:102_1_2"/>
<font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C2</font>
 <b>by </b><i>, <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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