<?xml version="1.0"?>
<div class="add">

<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>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>









<b>assume </b><a NAME="E1:40"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="rmod_2.html#M1">Submodule</a> of <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:40"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rmod_3.html#K1" target="_self">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rmod_3.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rmod_3.html#K1" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rmod_3.html#K2" target="_self">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rmod_3.html#K1" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="rmod_3.html#E49"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:40"/>
<font color="Maroon">c<sub>4</sub></font> <a href="rmod_3.html#K1" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rmod_3.html#K2" target="_self">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="rmod_3.html#K1" target="_self">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rmod_3.html#K2" target="_self">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rmod_3.html#K1" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="rmod_2.html#T37">RMOD_2:37</a></i>;<br/>


</div>
