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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>;<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>;<br/><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c5">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>;<br/>









<b>assume </b><a NAME="E1:55"/>
<font color="Maroon" title="c5">L</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font>
 ;<br/>

<a NAME="E2:55"/><b>then </b>
(  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c5">L</font> &amp;  <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <font color="Maroon" title="c5">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font> )
 
<b>by </b><i><a class="ref" href="rmod_4.html#D7" target="_self" title="RMOD_4:def.7">Def7</a>, <a class="ref" href="rmod_4.html#T58" target="_self" title="RMOD_4:th.58">Th58</a></i>;<br/>
<a NAME="E3:55"/><b>then </b>
 <a href="rmod_4.html#K2" title="RMOD_4:func.2">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:55"/>
<font color="Maroon" title="c5">L</font> <a href="rmod_4.html#K7" title="RMOD_4:func.7">*</a> <font color="Maroon" title="c3">a</font> is    <a href="rmod_4.html#M2" title="RMOD_4:mode.2">Linear_Combination</a> of <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="ref" href="rmod_4.html#D7" target="_self" title="RMOD_4:def.7">Def7</a></i>;<br/>


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