<?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">c</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">b</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="E1:8"/><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">d</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="realset2.html#K2">suppf</a> <font color="Maroon">F</font> &amp; <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">b</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="E2:8"/><b>then </b><i><font color="Green">E16</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">c</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> 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="realset2.html#T14">REALSET2:14</a></i>;<br/>
<a NAME="E3:8"/><i><font color="Green">E22</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">b</font></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"><font color="Maroon">c</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> implies <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">a</font>,<font color="Maroon">d</font> <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="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_1"/><i><font color="Green">E23</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">b</font></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"><font color="Maroon">c</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>
 ;<br/>

<i><font color="Green">E25</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">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">b</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"><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"><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">b</font></span>)</span>,<font color="Maroon">b</font></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#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="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">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">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, , <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"><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">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/>
<font color="Maroon">c</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">c</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">c</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"><font color="Maroon">c</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"><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>,<font color="Maroon">d</font></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#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="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">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">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span>,<font color="Maroon">d</font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, <a class="ref" href="realset2.html#T23">REALSET2:23</a></i>
;<br/>
<b>hence </b><a NAME="E4:8_1"/>
<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">a</font>,<font color="Maroon">d</font> <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="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 <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/>


</div><b>end;</b></div>
<a NAME="E4:8"/>
( <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">a</font>,<font color="Maroon">d</font> <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="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> implies <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">b</font></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"><font color="Maroon">c</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> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:8_2"/><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="binop_1.html#K2">.</a> <font color="Maroon">a</font>,<font color="Maroon">d</font> <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="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 ;<br/>

<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">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">d</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/>.= 
<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">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#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="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">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span>,<font color="Maroon">b</font></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/>
<b>hence </b><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">b</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="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">d</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">b</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="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">d</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span>)</span>,<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#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"><font color="Maroon">c</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>
<b>by </b><i><a class="ref" href="realset3.html#T2" target="_self">Th2</a>, <a class="ref" href="realset2.html#T25">REALSET2:25</a></i>
;<br/><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:8"/>
( <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">b</font></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"><font color="Maroon">c</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> iff <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">a</font>,<font color="Maroon">d</font> <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="binop_1.html#K2">.</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="realset3.html#T3" target="_self">Th3</a></i>;<br/>


</div>
