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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="ringcat1.html#V2" target="_self">strict</a>  <a href="ringcat1.html#L1" target="_self">RingMorphismStr</a> ;<br/>





<b>assume </b><a NAME="E1:18"/><i><font color="Green">E10</font></i>: 
(  <a href="ringcat1.html#K1" target="_self">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="ringcat1.html#K2" target="_self">cod</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="ringcat1.html#K3" target="_self">fun</a> <font color="Maroon">c<sub>3</sub></font> is <a href="ringcat1.html#V1" target="_self">linear</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="ringcat1.html#NM1">RingMorphism</a> <b>by </b><i><a class="ref" href="ringcat1.html#D6" target="_self">Def6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><a NAME="E1:18_1"/>
(  <a href="ringcat1.html#K1" target="_self">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="ringcat1.html#K2" target="_self">cod</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="ringcat1.html#E1:18"><i><font color="Green">E10</font></i></a></i>;<br/><b>hence </b><a NAME="E2:18_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="ringcat1.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="ringcat1.html#D8" target="_self">Def8</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:18"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is    <a href="ringcat1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="ringcat1.html#E1:18"><i><font color="Green">E10</font></i></a>, <a class="ref" href="ringcat1.html#D9" target="_self">Def9</a></i>;<br/>
<b>hence </b><a NAME="E5:18"/>
<font color="Maroon">c<sub>3</sub></font> is    <a href="ringcat1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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