<?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>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="mod_2.html#NM1">LModMorphism</a> of <font color="Maroon">c<sub>1</sub></font>,  <a href="mod_2.html#NM1">LModMorphism</a> of <font color="Maroon">c<sub>1</sub></font>] means  <a href="mod_2.html#K2" target="_self">dom</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#K3" target="_self">cod</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="mod_2.html#NM1">LModMorphism</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:28"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>]
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:28"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is    <a href="mod_2.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="mod_2.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E4:28"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#K2" target="_self">dom</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="mod_2.html#E3:28"><i><font color="Green">E18</font></i></a>, <a class="ref" href="mod_2.html#D11" target="_self">Def11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:28"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="mod_2.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="mod_2.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E7:28"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#K3" target="_self">cod</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="mod_2.html#E6:28"><i><font color="Green">E20</font></i></a>, <a class="ref" href="mod_2.html#D11" target="_self">Def11</a></i>;<br/>
<b>hence </b><a NAME="E8:28"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>2</sub></font> is    <a href="mod_2.html#M1" target="_self">Morphism</a> of <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> is    <a href="mod_2.html#M1" target="_self">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="mod_2.html#E1:28"><i><font color="Green">E17</font></i></a>, <a class="txt" href="mod_2.html#E3:28"><i><font color="Green">E18</font></i></a>, <a class="txt" href="mod_2.html#E4:28"><i><font color="Green">E19</font></i></a>, <a class="txt" href="mod_2.html#E6:28"><i><font color="Green">E20</font></i></a></i>;<br/>


</div>
