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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">V</font> being   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">K</font>  st <font color="Maroon" title="c1">K</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  holds <br/><font color="Olive" title="b1">V</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">K</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  implies <font color="Maroon" title="c2">V</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:8"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c1">K</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 <span class="kw">and </span><br/><a NAME="E2:8"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
 not <font color="Maroon" title="c2">V</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:8"/>
 ex <font color="Olive" title="b1">a</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font> st <font color="Olive" title="b1">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> <font color="Maroon" title="c2">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="struct_0.html#D18" title="STRUCT_0:def.18">STRUCT_0:def 18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="lmod_6.html#T5" target="_self" title="LMOD_6:th.5">Th5</a></span>; <a class="txt" 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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