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<b>let </b><font color="Maroon">F1</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font>, <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font>, <font color="Maroon">F2</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font>, <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:6_1_2"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">u1</font> being   <a href="unialg_3.html#M2" target="_self">Element</a> of  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font> holds  <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">u1</font> <a href="hidden.html#R1">=</a>  <a href="unialg_3.html#K4" target="_self">carr</a> <font color="Olive">u1</font>
 <b>and </b><br/><a NAME="E2:6_1_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">u2</font> being   <a href="unialg_3.html#M2" target="_self">Element</a> of  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font> holds  <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">u2</font> <a href="hidden.html#R1">=</a>  <a href="unialg_3.html#K4" target="_self">carr</a> <font color="Olive">u2</font>
 ;<br/>

<a NAME="E3:6_1_2"/>
for <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">u</font> <a href="hidden.html#R2">in</a>  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font> holds <br/><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">u</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:6_1_2_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">u1</font> = <font color="Maroon">u</font> as    <a href="unialg_3.html#M2" target="_self">Element</a> of  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">U0</font> ;<br/>
<b>consider </b><font color="Maroon">U1</font> being    <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">U0</font><b> such that </b><br/><a NAME="E4:6_1_2_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">u1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">U1</font> &amp;  <a href="unialg_3.html#K4" target="_self">carr</a> <font color="Maroon">u1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> )
 <b>by </b><i/>;<br/>
<a NAME="E5:6_1_2_1"/>
<font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">u1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:6_1_2_1"/>
<font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:6_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="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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