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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font>, <font color="Maroon" title="c3">G3</font>, <font color="Maroon" title="c4">G4</font> be   <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</a>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be  <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>  <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font>;<br/><b>let </b><font color="Maroon" title="c6">g</font> be  <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>  <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font>;<br/><b>let </b><font color="Maroon" title="c7">h</font> be  <a href="grcat_1.html#V2" title="GRCAT_1:attr.2">strict</a>  <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">G3</font>,<font color="Maroon" title="c4">G4</font>;<br/>







<b>consider </b><font color="Maroon" title="c8">f0</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font><b> such that </b><br/><a NAME="E2:48"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c8">f0</font> #)
 <b>by </b><i><a class="ref" href="grcat_1.html#T23" target="_self" title="GRCAT_1:th.23">Th23</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">g0</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font><b> such that </b><br/><a NAME="E4:48"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c3">G3</font>,<font color="Maroon" title="c9">g0</font> #)
 <b>by </b><i><a class="ref" href="grcat_1.html#T23" target="_self" title="GRCAT_1:th.23">Th23</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">h0</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">G3</font>,<font color="Maroon" title="c4">G4</font><b> such that </b><br/><a NAME="E6:48"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c7">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c3">G3</font>,<font color="Maroon" title="c4">G4</font>,<font color="Maroon" title="c10">h0</font> #)
 <b>by </b><i><a class="ref" href="grcat_1.html#T23" target="_self" title="GRCAT_1:th.23">Th23</a></i>;<br/>
<a NAME="E7:48"/><i><font color="Green" title="E30">A4</font></i>: 
<font color="Maroon" title="c6">g</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c3">G3</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f0</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="grcat_1.html#E2:48"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="grcat_1.html#E4:48"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="grcat_1.html#T29" target="_self" title="GRCAT_1:th.29">Th29</a></i>;<br/>
<a NAME="E8:48"/><i><font color="Green" title="E31">A5</font></i>: 
<font color="Maroon" title="c7">h</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c6">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c2">G2</font>,<font color="Maroon" title="c4">G4</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">h0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">g0</font></span>)</span> #)
 
<b>by </b><i><a class="txt" href="grcat_1.html#E4:48"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="grcat_1.html#E6:48"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="grcat_1.html#T29" target="_self" title="GRCAT_1:th.29">Th29</a></i>;<br/>
<font color="Maroon" title="c7">h</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c5">f</font></span>)</span> = 
 <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c4">G4</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">h0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">g0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f0</font></span>)</span></span>)</span> #)
<b>by </b><i><a class="txt" href="grcat_1.html#E6:48"><i><font color="Green" title="E29">A3</font></i></a>, <a class="txt" href="grcat_1.html#E7:48"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="grcat_1.html#T29" target="_self" title="GRCAT_1:th.29">Th29</a></i>
<br/>.= 
 <a href="grcat_1.html#G1" title="GRCAT_1:aggr.1">GroupMorphismStr</a>(# <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c4">G4</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">h0</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c9">g0</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c8">f0</font></span>)</span> #)
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c6">g</font></span>)</span> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c5">f</font>
<b>by </b><i><a class="txt" href="grcat_1.html#E2:48"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="grcat_1.html#E8:48"><i><font color="Green" title="E31">A5</font></i></a>, <a class="ref" href="grcat_1.html#T29" target="_self" title="GRCAT_1:th.29">Th29</a></i>
;<br/>
<b>hence </b><a NAME="E10:48"/>
<font color="Maroon" title="c7">h</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">h</font> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c6">g</font></span>)</span> <a href="grcat_1.html#K15" title="GRCAT_1:func.15">*</a> <font color="Maroon" title="c5">f</font>
 ;<br/>


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