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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font><br/> for <font color="Olive" title="b2">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Olive" title="b1">V</font> holds   <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Olive" title="b2">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Olive" title="b2">L</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font> holds   <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Olive" title="b1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Olive" title="b1">L</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be    <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Maroon" title="c3">L</font></span>)</span></span><br/>





<span class="kw">thus </span> <a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Maroon" title="c3">L</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="vectsp_2.html#K5" title="VECTSP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rmod_4.html#T78" target="_self" title="RMOD_4:th.78">Th78</a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K5" title="RMOD_4:func.5">Sum</a> <font color="Maroon" title="c3">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_2.html#T90" title="VECTSP_2:th.90">VECTSP_2:90</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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