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

<b>let </b><font color="Maroon">F</font> be   <a href="realset2.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font>, <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K4">ndf</a> <font color="Maroon">F</font></span>)</span></span><a href="realset1.html#K5">}</a></span>, <font color="Maroon">d</font> be    <a href="subset_1.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K4">ndf</a> <font color="Maroon">F</font></span>)</span></span><a href="realset1.html#K5">}</a></span>;<br/>





<a NAME="E1:11"/><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E2:11"/><i><font color="Green">E16</font></i>: 
<span class="p1">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:11"/>
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> is    <a href="subset_1.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K4">ndf</a> <font color="Maroon">F</font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 
<b>by </b><i><a class="ref" href="realset2.html#T28">REALSET2:28</a></i>;<br/>
<a NAME="E4:11"/><b>then </b>
<span class="p1">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span> is    <a href="subset_1.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K4">ndf</a> <font color="Maroon">F</font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 
<b>by </b><i><a class="ref" href="realset2.html#T28">REALSET2:28</a></i>;<br/>
<a NAME="E5:11"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span> is    <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font>
 
;<br/>
<i><font color="Green">E23</font></i>: <font color="Maroon">a</font> = 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="realset2.html#K6">nmf</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="realset2.html#T25">REALSET2:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">d</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="realset2.html#D15">REALSET2:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="realset3.html#T2" target="_self">Th2</a>, <a class="ref" href="realset2.html#T23">REALSET2:23</a></i>
;<br/>
<i><font color="Green">E25</font></i>: <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<span class="p2">(<span class="default"><a href="realset2.html#K6">nmf</a> <font color="Maroon">F</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="realset2.html#T25">REALSET2:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="realset2.html#D15">REALSET2:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, <a class="ref" href="realset2.html#T23">REALSET2:23</a></i>
;<br/>
<i><font color="Green">E26</font></i>: <span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span></span><a href="tarski.html#K4">]</a></span> = 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, <a class="ref" href="realset3.html#T2" target="_self">Th2</a>, , <a class="ref" href="realset2.html#T23">REALSET2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">d</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, <a class="ref" href="realset3.html#T2" target="_self">Th2</a>, <a class="ref" href="realset2.html#T24">REALSET2:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">d</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span> = 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, <a class="ref" href="realset3.html#T2" target="_self">Th2</a>, , <a class="ref" href="realset2.html#T23">REALSET2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E10:11"/>
<span class="p1">(<span class="default"><a href="realset2.html#K3">odf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">b</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K3">odf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">d</font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K8">revf</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="realset2.html#K5">omf</a> <font color="Maroon">F</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c</font>,<font color="Maroon">d</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="realset3.html#T3" target="_self">Th3</a>, <a class="ref" href="realset3.html#T4" target="_self">Th4</a>, <a class="ref" href="realset2.html#T3">REALSET2:3</a></i>;<br/>


</div>
