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<b>set </b><font color="Maroon">C</font> =  <a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font>;<br/>
<b>set </b><font color="Maroon">cF</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>;<br/>
<b>let </b><font color="Maroon">f1</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font>, <font color="Maroon">f2</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>,<span class="p2">(<span class="default"><a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:36_1_2"/><i><font color="Green">E75</font></i>: 
for <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font><br/> for <font color="Olive">A</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font><br/> for <font color="Olive">a</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="vectsp_4.html#K3">+</a> <font color="Maroon">W</font> holds <br/><font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Olive">z</font>,<font color="Olive">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">z</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">a</font></span>)</span> <a href="vectsp_4.html#K3">+</a> <font color="Maroon">W</font>
 <b>and </b><br/><a NAME="E2:36_1_2"/><i><font color="Green">E76</font></i>: 
for <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font><br/> for <font color="Olive">A</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font><br/> for <font color="Olive">a</font> being  <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="vectsp_4.html#K3">+</a> <font color="Maroon">W</font> holds <br/><font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Olive">z</font>,<font color="Olive">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">z</font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">a</font></span>)</span> <a href="vectsp_4.html#K3">+</a> <font color="Maroon">W</font>
 ;<br/>

<b>set </b><font color="Maroon">C</font> =  <a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font>;<br/><a NAME="E1:36_1_2_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="vectsp10.html#K2" target="_self">CosetSet</a> <font color="Maroon">V</font>,<font color="Maroon">W</font>
 ;<br/><b>then consider </b><font color="Maroon">A1</font> being    <a href="vectsp_4.html#M2">Coset</a> of <font color="Maroon">W</font><b> such that </b><br/><a NAME="E3:36_1_2_1"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/><b>consider </b><font color="Maroon">a</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E5:36_1_2_1"/><i><font color="Green">E101</font></i>: 
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="vectsp_4.html#K3">+</a> <font color="Maroon">W</font>
 <b>by </b><i><a class="ref" href="vectsp_4.html#D6">VECTSP_4:def 6</a></i>;<br/><b>thus </b><font color="Maroon">f1</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">z</font>,<font color="Maroon">A</font> = 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span> <a href="vectsp_4.html#K3">+</a> <font color="Maroon">W</font>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">z</font>,<font color="Maroon">A</font>
<b>by </b><i>, , </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:36_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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