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<b>let </b><font color="Maroon">f1</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">I</font>,<span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span>, <font color="Maroon">f2</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">I</font>,<span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">I</font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:96_1_2"/><i><font color="Green">E57</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font> holds  <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" target="_self">quotient</a> <font color="Olive">x</font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:96_1_2"/><i><font color="Green">E58</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font> holds  <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" target="_self">quotient</a> <font color="Olive">x</font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">I</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E3:96_1_2"/><i><font color="Green">E59</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:96_1_2"/><i><font color="Green">E60</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:96_1_2"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">I</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:96_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">I</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">I</font> ;<br/>
<font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> = 
 <a href="quofield.html#K12" target="_self">QClass.</a> <span class="p1">(<span class="default"><a href="quofield.html#K23" target="_self">quotient</a> <font color="Maroon">x</font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quofield.html#D8" target="_self">Def8</a></i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="quofield.html#D9" target="_self">Def9</a></i>
;<br/>
<b>hence </b><a NAME="E4:96_1_2_1"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:96_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="quofield.html#D10" target="_self">Def10</a>, <a class="ref" href="quofield.html#D11" target="_self">Def11</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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