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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="grcat_1.html#V2" target="_self">strict</a> <a href="grcat_1.html#NM1">GroupMorphism</a>;<br/>

<b>assume </b><a NAME="E1:51"/>
 <a href="grcat_1.html#K9" target="_self">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K10" target="_self">cod</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="mod_1.html#NM1">AddGroup</a>, <font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E3:51"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> #) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> #) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> #) )
 <b>by </b><i><a class="ref" href="grcat_1.html#T30" target="_self">Th30</a></i>;<br/>
<b>thus </b> <a href="grcat_1.html#K9" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="grcat_1.html#E3:51"><i><font color="Green">E30</font></i></a></i>
<br/>.= 
 <a href="grcat_1.html#K9" target="_self">dom</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="grcat_1.html#E3:51"><i><font color="Green">E30</font></i></a></i>
;<br/>

<b>thus </b> <a href="grcat_1.html#K10" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="grcat_1.html#E3:51"><i><font color="Green">E30</font></i></a></i>
<br/>.= 
 <a href="grcat_1.html#K10" target="_self">cod</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="grcat_1.html#E3:51"><i><font color="Green">E30</font></i></a></i>
;<br/>


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