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<b>let </b><font color="Maroon" title="c4">C1</font>, <font color="Maroon" title="c5">C2</font> be  <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a> <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">AbGroup</a>;<br/>

<b>assume </b><a NAME="E1:102_1_2"/><i><font color="Green" title="E66">A5</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K12" title="CHAIN_1:func.12">0_</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font> &amp; ( for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">C1</font><br/> for <font color="Olive" title="b3">A'</font>, <font color="Olive" title="b4">B'</font> being  <a href="chain_1.html#NM4" title="CHAIN_1:NM.4">Chain</a> of <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">A'</font> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">B'</font> holds <br/><font color="Olive" title="b1">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">A'</font> <a href="chain_1.html#K8" title="CHAIN_1:func.8">+</a> <font color="Olive" title="b4">B'</font> ) &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span> &amp;  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c5">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K12" title="CHAIN_1:func.12">0_</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font> &amp; ( for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">C2</font><br/> for <font color="Olive" title="b3">A'</font>, <font color="Olive" title="b4">B'</font> being  <a href="chain_1.html#NM4" title="CHAIN_1:NM.4">Chain</a> of <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">A'</font> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">B'</font> holds <br/><font color="Olive" title="b1">A</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">A'</font> <a href="chain_1.html#K8" title="CHAIN_1:func.8">+</a> <font color="Olive" title="b4">B'</font> ) )
 ;<br/>

<b>set </b><font color="Maroon" title="c6">X</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">op1</font> = the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c4">C1</font>, <font color="Maroon" title="c8">op2</font> = the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c5">C2</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span> <b>by </b><i><a class="txt" href="chain_1.html#E1:102_1_2"><i><font color="Green" title="E66">A5</font></i></a></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" title="c9">AB</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="chain_1.html#K1" title="CHAIN_1:func.1">bool</a> <span class="p3">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">cells</a> <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/><b>consider </b><font color="Maroon" title="c10">A'</font>, <font color="Maroon" title="c11">B'</font> being   <a href="chain_1.html#NM4" title="CHAIN_1:NM.4">Chain</a> of <font color="Maroon" title="c3">k</font>,<font color="Maroon" title="c2">G</font><b> such that </b><br/><a NAME="E2:102_1_2_1"/><i><font color="Green" title="E67">A6</font></i>: 
<font color="Maroon" title="c9">AB</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c10">A'</font>,<font color="Maroon" title="c11">B'</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c12">A1</font> = <font color="Maroon" title="c10">A'</font>, <font color="Maroon" title="c13">B1</font> = <font color="Maroon" title="c11">B'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">C1</font> <b>by </b><i><a class="txt" href="chain_1.html#E1:102_1_2"><i><font color="Green" title="E66">A5</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c14">A2</font> = <font color="Maroon" title="c10">A'</font>, <font color="Maroon" title="c15">B2</font> = <font color="Maroon" title="c11">B'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">C2</font> <b>by </b><i><a class="txt" href="chain_1.html#E1:102_1_2"><i><font color="Green" title="E66">A5</font></i></a></i>;<br/><b>thus </b><font color="Maroon" title="c7">op1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">AB</font> = 
<font color="Maroon" title="c12">A1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c13">B1</font>
<b>by </b><i><a class="txt" href="chain_1.html#E2:102_1_2_1"><i><font color="Green" title="E67">A6</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c10">A'</font> <a href="chain_1.html#K8" title="CHAIN_1:func.8">+</a> <font color="Maroon" title="c11">B'</font>
<b>by </b><i><a class="txt" href="chain_1.html#E1:102_1_2"><i><font color="Green" title="E66">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c14">A2</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c15">B2</font>
<b>by </b><i><a class="txt" href="chain_1.html#E1:102_1_2"><i><font color="Green" title="E66">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c8">op2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">AB</font>
<b>by </b><i><a class="txt" href="chain_1.html#E2:102_1_2_1"><i><font color="Green" title="E67">A6</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:102_1_2"/>
<font color="Maroon" title="c4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">C2</font>
 <b>by </b><i><a class="txt" href="chain_1.html#E1:102_1_2"><i><font color="Green" title="E66">A5</font></i></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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