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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_1.html#NM3">Scalar</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="vectsp_2.html#NM7">RightMod</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="vectsp_2.html#NM5">Vector</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="rmod_2.html#M1" target="_self">Submodule</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>









<b>assume </b><a NAME="E1:59"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E2:59"/><b>then </b><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="rmod_2.html#K3" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E70"><i><font color="Green">Lemma35</font></i></a></i>;<br/>
<a NAME="E3:59"/>
<font color="Maroon">c<sub>4</sub></font> <a href="vectsp_2.html#K6">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E1:59"><i><font color="Green">E42</font></i></a>, <a class="ref" href="rmod_2.html#T29" target="_self">Th29</a></i>;<br/>
<b>hence </b><a NAME="E4:59"/>
<font color="Maroon">c<sub>4</sub></font> <a href="vectsp_2.html#K6">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="rmod_2.html#K3" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E2:59"><i><font color="Green">E43</font></i></a>, <a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>


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