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

<b>let </b><font color="Maroon">f</font> be  <a href="ringcat1.html#V2" target="_self">strict</a> <a href="ringcat1.html#NM1">RingMorphism</a>, <font color="Maroon">g</font> be  <a href="ringcat1.html#V2" target="_self">strict</a> <a href="ringcat1.html#NM1">RingMorphism</a>;<br/>

<b>assume </b><a NAME="E1:31"/>
 <a href="ringcat1.html#K1" target="_self">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="ringcat1.html#K2" target="_self">cod</a> <font color="Maroon">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon">G1</font> being   <a href="funcsdom.html#NM1">Ring</a>, <font color="Maroon">G2</font> being   <a href="funcsdom.html#NM1">Ring</a>, <font color="Maroon">G3</font> being   <a href="funcsdom.html#NM1">Ring</a>, <font color="Maroon">f0</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G1</font>,<font color="Maroon">G2</font>, <font color="Maroon">g0</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G2</font>,<font color="Maroon">G3</font><b> such that </b><br/><a NAME="E3:31"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# <font color="Maroon">G1</font>,<font color="Maroon">G2</font>,<font color="Maroon">f0</font> #) &amp; <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# <font color="Maroon">G2</font>,<font color="Maroon">G3</font>,<font color="Maroon">g0</font> #) &amp; <font color="Maroon">g</font> <a href="ringcat1.html#K6" target="_self">*</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# <font color="Maroon">G1</font>,<font color="Maroon">G3</font>,<span class="p1">(<span class="default"><font color="Maroon">g0</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f0</font></span>)</span> #) )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E4:31"/>
 <a href="ringcat1.html#K1" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="ringcat1.html#K6" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ringcat1.html#K1" target="_self">dom</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E5:31"/>
 <a href="ringcat1.html#K2" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="ringcat1.html#K6" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ringcat1.html#K2" target="_self">cod</a> <font color="Maroon">g</font>
 <b>by </b><i/>;<br/>


</div>
