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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="grcat_1.html#NM1" title="GRCAT_1:NM.1">GroupMorphism</a>,  <a href="grcat_1.html#NM1" title="GRCAT_1:NM.1">GroupMorphism</a>] <b>means </b> <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> $2;<br/>
<b>let </b><font color="Maroon" title="c1">g</font>, <font color="Maroon" title="c2">f</font> be   <a href="grcat_1.html#NM1" title="GRCAT_1:NM.1">GroupMorphism</a>;<br/>

<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c1">g</font>,<font color="Maroon" title="c2">f</font>]
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">G2</font>, <font color="Maroon" title="c4">G3</font> being   <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</a><b> such that </b><br/><a NAME="E3:41"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c1">g</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">G2</font>,<font color="Maroon" title="c4">G3</font>
 <b>by </b><i><a class="ref" href="grcat_1.html#T24" target="_self" title="GRCAT_1:th.24">Th24</a></i>;<br/>
<a NAME="E4:41"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c3">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K8" title="GRCAT_1:func.8">dom</a> <font color="Maroon" title="c1">g</font>
 
<b>by </b><i><a class="txt" href="grcat_1.html#E3:41"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">G1</font>, <font color="Maroon" title="c6">G2'</font> being   <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</a><b> such that </b><br/><a NAME="E6:41"/><i><font color="Green" title="E24">A4</font></i>: 
<font color="Maroon" title="c2">f</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c5">G1</font>,<font color="Maroon" title="c6">G2'</font>
 <b>by </b><i><a class="ref" href="grcat_1.html#T24" target="_self" title="GRCAT_1:th.24">Th24</a></i>;<br/>
<a NAME="E7:41"/>
<font color="Maroon" title="c6">G2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="grcat_1.html#K9" title="GRCAT_1:func.9">cod</a> <font color="Maroon" title="c2">f</font>
 
<b>by </b><i><a class="txt" href="grcat_1.html#E6:41"><i><font color="Green" title="E24">A4</font></i></a>, <a class="ref" href="grcat_1.html#D19" target="_self" title="GRCAT_1:def.19">Def19</a></i>;<br/>
<b>hence </b><a NAME="E8:41"/>
 ex <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font>, <font color="Olive" title="b3">G3</font> being  <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">AddGroup</a> st <br/>( <font color="Maroon" title="c1">g</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Olive" title="b2">G2</font>,<font color="Olive" title="b3">G3</font> &amp; <font color="Maroon" title="c2">f</font> is    <a href="grcat_1.html#M1" title="GRCAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E1:41"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="grcat_1.html#E3:41"><i><font color="Green" title="E22">A2</font></i></a>, <a class="txt" href="grcat_1.html#E4:41"><i><font color="Green" title="E23">A3</font></i></a>, <a class="txt" href="grcat_1.html#E6:41"><i><font color="Green" title="E24">A4</font></i></a></i>;<br/>


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