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<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#V2" title="RINGCAT1:attr.2">strict</a>  <a href="ringcat1.html#L1" title="RINGCAT1:struct.1">RingMorphismStr</a> ;<br/>





<b>assume </b><a NAME="E1:19"/><i><font color="Green" title="E10">A1</font></i>: 
(  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> &amp;  <a href="ringcat1.html#K3" title="RINGCAT1:func.3">fun</a> <font color="Maroon" title="c3">f</font> is <a href="ringcat1.html#V1" title="RINGCAT1:attr.1">linear</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">f'</font> = <font color="Maroon" title="c3">f</font> as   <a href="ringcat1.html#NM1" title="RINGCAT1:NM.1">RingMorphism</a> <b>by </b><i><a class="ref" href="ringcat1.html#D6" target="_self" title="RINGCAT1:def.6">Def6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>now </b></a><div class="add"><a NAME="E1:19_1"/>
(  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <font color="Maroon" title="c4">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <font color="Maroon" title="c4">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H</font> )
 <b>by </b><i><a class="txt" href="ringcat1.html#E1:19"><i><font color="Green" title="E10">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E2:19_1"/>
<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>
 <b>by </b><i><a class="ref" href="ringcat1.html#D8" target="_self" title="RINGCAT1:def.8">Def8</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:19"/><b>then </b>
<font color="Maroon" title="c4">f'</font> is    <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>
 
<b>by </b><i><a class="txt" href="ringcat1.html#E1:19"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="ringcat1.html#D9" target="_self" title="RINGCAT1:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E5:19"/>
<font color="Maroon" title="c3">f</font> is    <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/>


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