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<span class="kw">consider </span><font color="Maroon" title="c1">V</font> being   <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a>, <font color="Maroon" title="c2">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a><span class="kw"> such that </span><br/><a NAME="E2:70_1_1"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
( <font color="Maroon" title="c2">p</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> &amp;  not  <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">p</font> <a href="zmodul02.html#K5" title="ZMODUL02:func.5">(*)</a> <font color="Maroon" title="c1">V</font></span>)</span>) is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul07.html#T43" target="_self" onmouseover="rs('zmodul07/T43')" onmouseout="rh()">LMCLUS1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">pp</font> = <font color="Maroon" title="c2">p</font> as   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:70_1_1"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="ref" href="struct_0.html#D12" onmouseover="rs('struct_0/D12')" onmouseout="rh()">STRUCT_0:def 12</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">W</font> =  <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="c3">pp</font> <a href="zmodul02.html#K5" title="ZMODUL02:func.5">(*)</a> <font color="Maroon" title="c1">V</font></span>)</span>);<br/>
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 not  <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="c3">pp</font> <a href="zmodul02.html#K5" title="ZMODUL02:func.5">(*)</a> <font color="Maroon" title="c1">V</font></span>)</span>) is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:70_1_1"><span class="lab"><font color="Green" title="E39">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:70_1_1"/>
 not  for <font color="Olive">b<sub>1</sub></font> being   <a href="zmodul06.html#V2" title="ZMODUL06:attr.2">torsion</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a> holds  <font color="Olive">b<sub>1</sub></font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</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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