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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   non  <a href="zmodul06.html#V3" title="ZMODUL06:attr.3">torsion-free</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</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">  not <font color="Maroon" title="c1">V</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/>

<span class="kw">assume </span><a NAME="E1:75_1_1"/>
<font color="Maroon" title="c1">V</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"> contradiction</span><br/>

<a NAME="E2:75_1_1"/><span class="kw">then </span>
 <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul07.html#T41" target="_self" onmouseover="rs('zmodul07/T41')" onmouseout="rh()">ThTrivial1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:75_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zmodul07.html#T44" target="_self" onmouseover="rs('zmodul07/T44')" onmouseout="rh()">ThTFX</a></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"> verum</span><br/>


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