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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="struct_0.html#NM6">Function</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>;<br/>





<b>assume </b><a NAME="E1:19"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">f</font> is <a href="ringcat1.html#V1" target="_self">linear</a>
 ;<br/>

<b>set </b><font color="Maroon">F</font> =  <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# <font color="Maroon">G</font>,<font color="Maroon">H</font>,<font color="Maroon">f</font> #);<br/>
<a NAME="E2:19"/>
(  <a href="ringcat1.html#K1" target="_self">dom</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> #) <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> &amp;  <a href="ringcat1.html#K2" target="_self">cod</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> #) <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> &amp;  <a href="ringcat1.html#K3" target="_self">fun</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> #) <a href="funct_2.html#R1">=</a> <font color="Maroon">f</font> )
 
;<br/>
<b>hence </b><a NAME="E3:19"/>
 <a href="ringcat1.html#G1" target="_self">RingMorphismStr</a>(# <font color="Maroon">G</font>,<font color="Maroon">H</font>,<font color="Maroon">f</font> #) is    <a href="ringcat1.html#M1" target="_self">Morphism</a> of <font color="Maroon">G</font>,<font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/>


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