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

<b>thus </b><a NAME="E1:7_1"/>
( <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() implies <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()] )
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()] implies <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_1"/>
<font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()]</span><br/>

<a NAME="E2:7_1_1"/><b>then </b><i><font color="Green" title="E2">A2</font></i>: 
<font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">a</font>] </span>}</span> 
 
<b>by </b><i><a class="txt" href="#E1:7"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<b>thus </b><a NAME="E3:7_1_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()]
 <b>from </b><i><a class="ref" href="lmod_7.html#S6" target="_self" title="LMOD_7:sch.6">LMOD_7:sch 6</a>(<a class="txt" href="#E2:7_1_1"><i><font color="Green" title="E2">A2</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>assume </b><a NAME="E2:7_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">F<sub>3</sub></font>()]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()</span><br/>

<b>hence </b><a NAME="E3:7_1"/>
<font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i><a class="txt" href="#E1:7"><i><font color="Green" title="E1">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
