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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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">L1</font>, <font color="Olive" title="b3">L2</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Olive" title="b3">L2</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a>  <a href="rmod_4.html#K3" title="RMOD_4:func.3">ZeroLC</a> <font color="Olive" title="b1">V</font> holds <br/><font color="Olive" title="b3">L2</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a>  <a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Olive" title="b2">L1</font></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">L2</font> being   <a href="rmod_4.html#M1" title="RMOD_4:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Olive" title="b2">L2</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a>  <a href="rmod_4.html#K3" title="RMOD_4:func.3">ZeroLC</a> <font color="Maroon" title="c2">V</font> holds <br/><font color="Olive" title="b2">L2</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a>  <a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Olive" title="b1">L1</font></span><br/><b>let </b><font color="Maroon" title="c3">L1</font>, <font color="Maroon" title="c4">L2</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Maroon" title="c4">L2</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a>  <a href="rmod_4.html#K3" title="RMOD_4:func.3">ZeroLC</a> <font color="Maroon" title="c2">V</font> implies <font color="Maroon" title="c4">L2</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a>  <a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Maroon" title="c3">L1</font> )</span><br/>







<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c3">L1</font> <a href="rmod_4.html#K6" title="RMOD_4:func.6">+</a> <font color="Maroon" title="c4">L2</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a>  <a href="rmod_4.html#K3" title="RMOD_4:func.3">ZeroLC</a> <font color="Maroon" title="c2">V</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">L2</font> <a href="rmod_4.html#R1" title="RMOD_4:pred.1">=</a>  <a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Maroon" title="c3">L1</font></span><br/>

<b>let </b><font color="Maroon" title="c5">v</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="rmod_4.html#D10" target="_self" title="RMOD_4:def.10">RMOD_4:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">L2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Maroon" title="c3">L1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span><br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="rmod_4.html#K3" title="RMOD_4:func.3">ZeroLC</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="txt" href="rmod_4.html#E1:61"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="rmod_4.html#D11" target="_self" title="RMOD_4:def.11">Def11</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">R</font>
<b>by </b><i><a class="ref" href="rmod_4.html#T22" target="_self" title="RMOD_4:th.22">Th22</a></i>
;<br/>
<b>hence </b><font color="Maroon" title="c4">L2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font> = 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T19" title="RLVECT_1:th.19">RLVECT_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rmod_4.html#K8" title="RMOD_4:func.8">-</a> <font color="Maroon" title="c3">L1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="ref" href="rmod_4.html#T67" target="_self" title="RMOD_4:th.67">Th67</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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