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

<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c3">F</font> be    <a href="ringcat1.html#M1" title="RINGCAT1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>;<br/>





<b>assume </b><a NAME="E1:24"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="ringcat1.html#R1" title="RINGCAT1:pred.1">&lt;=</a> <font color="Maroon" title="c2">H</font>
 ;<br/>

<i><font color="Green" title="E16">A2</font></i>: the <a href="ringcat1.html#U1" title="RINGCAT1:sel.1">Dom</a> of <font color="Maroon" title="c3">F</font> = 
 <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <font color="Maroon" title="c3">F</font>

<br/>.= 
<font color="Maroon" title="c1">G</font>
<b>by </b><i><a class="txt" href="ringcat1.html#E1:24"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="ringcat1.html#D9" target="_self" title="RINGCAT1:def.9">Def9</a></i>
;<br/>
<i><font color="Green" title="E17">A3</font></i>: the <a href="ringcat1.html#U2" title="RINGCAT1:sel.2">Cod</a> of <font color="Maroon" title="c3">F</font> = 
 <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <font color="Maroon" title="c3">F</font>

<br/>.= 
<font color="Maroon" title="c2">H</font>
<b>by </b><i><a class="txt" href="ringcat1.html#E1:24"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="ringcat1.html#D9" target="_self" title="RINGCAT1:def.9">Def9</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">f</font> = the <a href="ringcat1.html#U3" title="RINGCAT1:sel.3">Fun</a> of <font color="Maroon" title="c3">F</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font> <b>by </b><i><a class="txt" href="ringcat1.html#E2:24"><i><font color="Green" title="E16">A2</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">f</font>
;<br/>

<b>thus </b><a NAME="E5:24"/>
( <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#G1" title="RINGCAT1:aggr.1">RingMorphismStr</a>(# <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c4">f</font> #) &amp; <font color="Maroon" title="c4">f</font> is <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )
 <b>by </b><i><a class="txt" href="ringcat1.html#E2:24"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="ringcat1.html#E3:24"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="ringcat1.html#E15"><i><font color="Green" title="E8">Lm3</font></i></a></i>;<br/>


</div>
