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

<b>thus </b><a NAME="E1:10_1"/>
( <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon">F<sub>3</sub></font>()) implies for <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>4</sub></font>(),<font color="Olive">b</font>] )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1"><b>proof </b></a><div class="add">

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">F<sub>3</sub></font>()];<br/>
<b>assume </b><a NAME="E1:10_1_1"/>
<font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon">F<sub>3</sub></font>())
 ;<br/>

<a NAME="E2:10_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">a</font> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] </span>}</span> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:10_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">F<sub>4</sub></font>()]
 
<b>from </b><i><a class="ref" href="lmod_7.html#S6" target="_self">LMOD_7:sch 6</a>();<br/></i>
<b>hence </b><a NAME="E4:10_1_1"/>
for <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>4</sub></font>(),<font color="Olive">b</font>]
 <b>by </b><i/>;<br/>


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

<b>assume </b><a NAME="E2:10_1"/>
for <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>3</sub></font>() holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>4</sub></font>(),<font color="Olive">b</font>]
 ;<br/>

<b>hence </b><a NAME="E3:10_1"/>
<font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>5</sub></font>(<font color="Maroon">F<sub>3</sub></font>())
 <b>by </b><i>, </i>;<br/>


</div>
