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<a NAME="E1:11_1"/><i><font color="Green">E18</font></i>: 
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> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_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="E1:11_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ;<br/>

<a NAME="E2:11_1_1"/><b>then </b>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x</font>]
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:11_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E2:11_1"/>
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> <font color="Maroon">F<sub>2</sub></font>() holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_2"><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="E1:11_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>()
 ;<br/>

<a NAME="E2:11_1_2"/><b>then </b>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">x</font>]
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:11_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:11_1"/>
<font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>()
 <b>by </b><i>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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