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<b>let </b><font color="Maroon">G1</font> be   <a href="mod_1.html#NM1">AddGroup</a>, <font color="Maroon">G2</font> be   <a href="mod_1.html#NM1">AddGroup</a>, <font color="Maroon">G3</font> be   <a href="mod_1.html#NM1">AddGroup</a>, <font color="Maroon">G4</font> be   <a href="mod_1.html#NM1">AddGroup</a>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="grcat_1.html#V2" target="_self">strict</a>  <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">G1</font>,<font color="Maroon">G2</font>;<br/><b>let </b><font color="Maroon">g</font> be  <a href="grcat_1.html#V2" target="_self">strict</a>  <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">G2</font>,<font color="Maroon">G3</font>;<br/><b>let </b><font color="Maroon">h</font> be  <a href="grcat_1.html#V2" target="_self">strict</a>  <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">G3</font>,<font color="Maroon">G4</font>;<br/>







<b>consider </b><font color="Maroon">f0</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G1</font>,<font color="Maroon">G2</font><b> such that </b><br/><a NAME="E2:52"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">G1</font>,<font color="Maroon">G2</font>,<font color="Maroon">f0</font> #)
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">g0</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G2</font>,<font color="Maroon">G3</font><b> such that </b><br/><a NAME="E4:52"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">G2</font>,<font color="Maroon">G3</font>,<font color="Maroon">g0</font> #)
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">h0</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">G3</font>,<font color="Maroon">G4</font><b> such that </b><br/><a NAME="E6:52"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">G3</font>,<font color="Maroon">G4</font>,<font color="Maroon">h0</font> #)
 <b>by </b><i/>;<br/>
<a NAME="E7:52"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">g</font> <a href="grcat_1.html#K16" target="_self">*</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">G1</font>,<font color="Maroon">G3</font>,<span class="p1">(<span class="default"><font color="Maroon">g0</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f0</font></span>)</span> #)
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E8:52"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">h</font> <a href="grcat_1.html#K16" target="_self">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">G2</font>,<font color="Maroon">G4</font>,<span class="p1">(<span class="default"><font color="Maroon">h0</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g0</font></span>)</span> #)
 
<b>by </b><i>, , </i>;<br/>
<font color="Maroon">h</font> <a href="grcat_1.html#K16" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="grcat_1.html#K16" target="_self">*</a> <font color="Maroon">f</font></span>)</span> = 
 <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">G1</font>,<font color="Maroon">G4</font>,<span class="p1">(<span class="default"><font color="Maroon">h0</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">g0</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f0</font></span>)</span></span>)</span> #)
<b>by </b><i>, , </i>
<br/>.= 
 <a href="grcat_1.html#G1" target="_self">GroupMorphismStr</a>(# <font color="Maroon">G1</font>,<font color="Maroon">G4</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">h0</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g0</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">f0</font></span>)</span> #)
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="grcat_1.html#K16" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="grcat_1.html#K16" target="_self">*</a> <font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="grcat_1.html#T4" target="_self">Th4</a>, </i>
;<br/>
<b>hence </b><a NAME="E10:52"/>
<font color="Maroon">h</font> <a href="grcat_1.html#K16" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="grcat_1.html#K16" target="_self">*</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="grcat_1.html#K16" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="grcat_1.html#K16" target="_self">*</a> <font color="Maroon">f</font>
 ;<br/>


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