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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</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">  for <font color="Olive" title="b1">V</font> being   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">RightMod</a> of <font color="Maroon" title="c1">R</font> holds   <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">V</font> is  <a href="rmod_4.html#V1" title="RMOD_4:attr.1">linearly-independent</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">RightMod</a> of <font color="Maroon" title="c1">R</font>; <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">  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font> is  <a href="rmod_4.html#V1" title="RMOD_4:attr.1">linearly-independent</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">l</font> be    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rmod_4.html#D13" target="_self" onmouseover="rs('rmod_4/D13')" onmouseout="rh()">RMOD_4:def 13</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"> (  <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> implies  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>





<a NAME="E1:76"/>
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c3">l</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#D5" target="_self" onmouseover="rs('rmod_4/D5')" onmouseout="rh()">Def5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:76"/>
(  <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> implies  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c3">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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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