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<span class="kw">set </span><font color="Maroon" title="c3">W</font> = <font color="Maroon" title="c2">a</font> <a href="zmodul02.html#K5" title="ZMODUL02:func.5">(*)</a> <font color="Maroon" title="c1">V</font>;<br/>
<a NAME="E1:66_1_1"/>
 for <font color="Olive" title="b1">x</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="zmodul02.html#K5" title="ZMODUL02:func.5">(*)</a> <font color="Maroon" title="c1">V</font></span>)</span>)</span>)</span> holds  <font color="Olive" title="b1">x</font> is  <a href="zmodul06.html#V1" title="ZMODUL06:attr.1">torsion</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="66_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="zmodul02.html#K5" title="ZMODUL02:func.5">(*)</a> <font color="Maroon" title="c1">V</font></span>)</span>)</span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">x</font> is  <a href="zmodul06.html#V1" title="ZMODUL06:attr.1">torsion</a> </span><br/>

<a NAME="E1:66_1_1_1"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>
 
;<br/>
<a NAME="E2:66_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
;<br/>
<span class="kw">then </span><font color="Maroon" title="c2">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c4">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="int_3.html#K5" title="INT_3:func.5">mod</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c4">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul02.html#T2" onmouseover="rs('zmodul02/T2')" onmouseout="rh()">ZMODUL02:2</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="zmodul02.html#K5" title="ZMODUL02:func.5">(*)</a> <font color="Maroon" title="c1">V</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T50" onmouseover="rs('int_1/T50')" onmouseout="rh()">INT_1:50</a>, <a class="ref" href="zmodul01.html#T1" onmouseover="rs('zmodul01/T1')" onmouseout="rh()">ZMODUL01:1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:66_1_1_1"/>
<font color="Maroon" title="c4">x</font> is  <a href="zmodul06.html#V1" title="ZMODUL06:attr.1">torsion</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:66_1_1"/>
 <a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> (<font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="zmodul02.html#K5" title="ZMODUL02:func.5">(*)</a> <font color="Maroon" title="c1">V</font></span>)</span>) is  <a href="zmodul06.html#V2" title="ZMODUL06:attr.2">torsion</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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