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<b>let </b><font color="Maroon">G</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="ringcat1.html#M1" target="_self">Morphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>;<br/>





<b>assume </b><a NAME="E1:23"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">G</font> <a href="ringcat1.html#R1" target="_self">&lt;=</a> <font color="Maroon">H</font>
 ;<br/>

<i><font color="Green">E32</font></i>: the <a href="ringcat1.html#U1" target="_self">Dom</a> of <font color="Maroon">F</font> = 
 <a href="ringcat1.html#K1" target="_self">dom</a> <font color="Maroon">F</font>

<br/>.= 
<font color="Maroon">G</font>
<b>by </b><i>, </i>
;<br/>
<i><font color="Green">E34</font></i>: the <a href="ringcat1.html#U2" target="_self">Cod</a> of <font color="Maroon">F</font> = 
 <a href="ringcat1.html#K2" target="_self">cod</a> <font color="Maroon">F</font>

<br/>.= 
<font color="Maroon">H</font>
<b>by </b><i>, </i>
;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = the <a href="ringcat1.html#U3" target="_self">Fun</a> of <font color="Maroon">F</font> as   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E5:23"/>
( <font color="Maroon">F</font> <a href="hidden.html#R1">=</a>  <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# <font color="Maroon">G</font>,<font color="Maroon">H</font>,<font color="Maroon">f</font> #) &amp; <font color="Maroon">f</font> is <a href="ringcat1.html#V1" target="_self">linear</a> )
 <b>by </b><i>, , </i>;<br/>


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