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<b>let </b><font color="Maroon">G1</font> be   <a href="group_1.html#NM1">Group</a>;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font>) <b>-&gt; </b>  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" target="_self">product</a> <span class="p2"><a href="group_7.html#K4" target="_self">&lt;*</a><span class="default"><font color="Maroon">G1</font></span><a href="group_7.html#K4" target="_self">*&gt;</a></span></span>)</span> = <span class="p1"><a href="group_7.html#K10" target="_self">&lt;*</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="group_7.html#K10" target="_self">*&gt;</a></span>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="group_7.html#K2" target="_self">product</a> <span class="p2"><a href="group_7.html#K8" target="_self">&lt;*</a><span class="default"><font color="Maroon">G1</font></span><a href="group_7.html#K8" target="_self">*&gt;</a></span></span>)</span><b> such that </b><br/><a NAME="E2:87"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G1</font> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G1</font>,<span class="p1">(<span class="default"><a href="group_7.html#K2" target="_self">product</a> <span class="p2"><a href="group_7.html#K8" target="_self">&lt;*</a><span class="default"><font color="Maroon">G1</font></span><a href="group_7.html#K8" target="_self">*&gt;</a></span></span>)</span> <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D15">GROUP_6:def 15</a><br/>

<b>thus </b><a NAME="E4:87"/>
<font color="Maroon">f</font> is <a href="group_6.html#V4">being_isomorphism</a>
 <b>by </b><i>, <a class="ref" href="group_7.html#D1" target="_self">Def1</a></i>;<br/>


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