<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">U0</font> be  <a href="unialg_1.html#V3">strict</a> <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font>;<br/>



<b>thus </b><a NAME="E1:13"/>
( <font color="Maroon">A</font> is    <a href="freealg.html#M1" target="_self">GeneratorSet</a> of <font color="Maroon">U0</font> implies  <a href="unialg_2.html#K7">GenUnivAlg</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">U0</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1"/>
<font color="Maroon">A</font> is    <a href="freealg.html#M1" target="_self">GeneratorSet</a> of <font color="Maroon">U0</font>
 ;<br/>

<a NAME="E2:13_1"/><b>then </b><i><font color="Green">E32</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="unialg_2.html#K7">GenUnivAlg</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U0</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:13_1"/>
<font color="Maroon">U0</font> is  <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">U0</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#T11">UNIALG_2:11</a></i>;<br/>
<b>hence </b><a NAME="E4:13_1"/>
 <a href="unialg_2.html#K7">GenUnivAlg</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">U0</font>
 <b>by </b><i>, <a class="ref" href="unialg_2.html#T15">UNIALG_2:15</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:13"/>
 <a href="unialg_2.html#K7">GenUnivAlg</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">U0</font>
 ;<br/>

<b>hence </b><a NAME="E3:13"/>
<font color="Maroon">A</font> is    <a href="freealg.html#M1" target="_self">GeneratorSet</a> of <font color="Maroon">U0</font>
 <b>by </b><i/>;<br/>


</div>
