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<b>let </b><font color="Maroon">f</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/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:15_1_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#R2">=</a>  <a href="unialg_3.html#K5" target="_self">Carr</a> <font color="Maroon">U0</font>
 ;<br/><b>let </b><font color="Maroon">u</font> be    <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>let </b><font color="Maroon">U1</font> be    <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">U0</font>;<br/><b>assume </b><a NAME="E2:15_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">U1</font>
 ;<br/><a NAME="E3:15_1_1_1"/>
 ex <font color="Olive">U2</font> being   <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">U0</font> st <br/>( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Olive">U2</font> &amp;  <a href="unialg_3.html#K4" target="_self">carr</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">U2</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:15_1_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">u</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/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:15_1_1"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">u</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><br/> for <font color="Olive">U1</font> being   <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">U0</font>  st <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Olive">U1</font> holds <br/><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">u</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">U1</font>
 ;<br/>

<a NAME="E3:15_1_1"/>
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">f</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <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>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/>
<a NAME="E2:15_1_1_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">u</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/>
<b>hence </b><a NAME="E3:15_1_1_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="unialg_3.html#K4" target="_self">carr</a> <font color="Maroon">u</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#R2">=</a>  <a href="unialg_3.html#K5" target="_self">Carr</a> <font color="Maroon">U0</font>
 <b>by </b><i/>;<br/>


</div>
