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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="vectsp_2.html#NM7">RightMod</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="rmod_4.html#M1" target="_self">Linear_Combination</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><a NAME="E1:47"/>
( <font color="Maroon">c<sub>4</sub></font> is    <a href="rmod_4.html#M2" target="_self">Linear_Combination</a> of <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is    <a href="rmod_4.html#M2" target="_self">Linear_Combination</a> of <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:47"/><b>then </b>
(  <a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="rmod_4.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E3:47"/><b>then </b>
( <span class="p1">(<span class="default"><a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="rmod_4.html#K2" target="_self">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rmod_4.html#K6" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="rmod_4.html#K2" target="_self">Carrier</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="rmod_4.html#T51" target="_self">Th51</a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E4:47"/>
 <a href="rmod_4.html#K2" target="_self">Carrier</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rmod_4.html#K6" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="rmod_4.html#D7" target="_self">RMOD_4:def 7</a><br/>


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