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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="mod_1.html#NM1">AddGroup</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E2:47"/><i><font color="Green">E27</font></i>: 
 <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# the <a href="grcat_1.html#U1" target="_self">Dom</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="grcat_1.html#U2" target="_self">Cod</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="grcat_1.html#U3" target="_self">Fun</a> of <font color="Maroon">c<sub>4</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> #)
 <b>and </b><br/><a NAME="E3:47"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="grcat_1.html#V1" target="_self">additive</a>
 <b>by </b><i><a class="ref" href="grcat_1.html#T22" target="_self">Th22</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E5:47"/><i><font color="Green">E28</font></i>: 
 <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# the <a href="grcat_1.html#U1" target="_self">Dom</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="grcat_1.html#U2" target="_self">Cod</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="grcat_1.html#U3" target="_self">Fun</a> of <font color="Maroon">c<sub>5</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>7</sub></font> #)
 <b>and </b><br/><a NAME="E6:47"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="grcat_1.html#V1" target="_self">additive</a>
 <b>by </b><i><a class="ref" href="grcat_1.html#T22" target="_self">Th22</a></i>;<br/>
 <a href="grcat_1.html#K9" target="_self">dom</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="grcat_1.html#D19" target="_self">Def19</a></i>
<br/>.= 
 <a href="grcat_1.html#K10" target="_self">cod</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="grcat_1.html#D19" target="_self">Def19</a></i>
;<br/>
<a NAME="E8:47"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="grcat_1.html#E2:47"><i><font color="Green">E27</font></i></a>, <a class="txt" href="grcat_1.html#E5:47"><i><font color="Green">E28</font></i></a>, <a class="ref" href="grcat_1.html#D21" target="_self">Def21</a></i>;<br/>
<a NAME="E9:47"/><b>then </b>
(  <a href="grcat_1.html#K9" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="grcat_1.html#K10" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E10:47"/>
<font color="Maroon">c<sub>4</sub></font> <a href="grcat_1.html#K15" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> is    <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="grcat_1.html#D19" target="_self">Def19</a></i>;<br/>


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