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

<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font><br/> for <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">d</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds <br/> ( <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">d</font></span>)</span> iff <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b2">c</font> )</span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">d</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds <br/> ( <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">d</font></span>)</span> iff <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Olive" title="b2">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">b</font>,<font color="Maroon" title="c3">c</font> )</span><br/><b>let </b><font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">d</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font></span>)</span> iff <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font> )</span><br/>





<a NAME="E1:5"/><i><font color="Green" title="E6">A1</font></i>: 
( <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font></span>)</span> implies <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon" title="c6">revfb</font> = <span class="p1">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c7">revfd</font> = <span class="p1">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">crevfd</font> = <font color="Maroon" title="c3">c</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">revfd</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> ;<br/>
<b>assume </b><a NAME="E3:5_1"/><i><font color="Green" title="E7">A2</font></i>: 
<span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font></span><br/>

<i><font color="Green" title="E8">A3</font></i>: <font color="Maroon" title="c2">a</font> = 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T25" title="REALSET2:th.25">REALSET2:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">revfb</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#D18" title="REALSET2:def.18">REALSET2:def 18</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">revfb</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">b</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">revfb</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">b</font>
<b>by </b><i><a class="ref" href="realset2.html#T23" title="REALSET2:th.23">REALSET2:23</a></i>
<br/>.= 
<font color="Maroon" title="c4">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c8">crevfd</font>
<b>by </b><i><a class="txt" href="realset3.html#E3:5_1"><i><font color="Green" title="E7">A2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">b</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font></span>)</span></span>)</span>

;<br/>
<i><font color="Green" title="E9">A4</font></i>: <font color="Maroon" title="c3">c</font> = 
<font color="Maroon" title="c3">c</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T25" title="REALSET2:th.25">REALSET2:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">d</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">revfd</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#D18" title="REALSET2:def.18">REALSET2:def 18</a></i>
<br/>.= 
<font color="Maroon" title="c3">c</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">revfd</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">d</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">revfd</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="ref" href="realset2.html#T23" title="REALSET2:th.23">REALSET2:23</a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">revfd</font></span>)</span></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="txt" href="realset3.html#E4:5_1"><i><font color="Green" title="E8">A3</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">revfd</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">d</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T23" title="REALSET2:th.23">REALSET2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font>
<b>by </b><i><a class="txt" href="realset3.html#E5:5_1"><i><font color="Green" title="E9">A4</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>
<a NAME="E2:5"/>
( <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font> implies <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon" title="c6">revfd</font> = <span class="p1">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font>, <font color="Maroon" title="c7">revfb</font> = <span class="p1">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">crevfd</font> = <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">revfd</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font> ;<br/>
<b>assume </b><a NAME="E3:5_2"/><i><font color="Green" title="E7">A5</font></i>: 
<span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font></span>)</span></span><br/>

<font color="Maroon" title="c2">a</font> = 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T25" title="REALSET2:th.25">REALSET2:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>

<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">d</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">revfd</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#D18" title="REALSET2:def.18">REALSET2:def 18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">revfd</font>
<b>by </b><i><a class="ref" href="realset2.html#T23" title="REALSET2:th.23">REALSET2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">revfd</font>
<b>by </b><i><a class="txt" href="realset3.html#E3:5_2"><i><font color="Green" title="E7">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c6">revfd</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T23" title="REALSET2:th.23">REALSET2:23</a></i>
<br/>.= 
<font color="Maroon" title="c8">crevfd</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">b</font>

;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">crevfd</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">revfb</font>

<br/>.= 
<font color="Maroon" title="c8">crevfd</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">b</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Maroon" title="c7">revfb</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T23" title="REALSET2:th.23">REALSET2:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">revfd</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#D18" title="REALSET2:def.18">REALSET2:def 18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font></span>)</span>
<b>by </b><i><a class="ref" href="realset2.html#T25" title="REALSET2:th.25">REALSET2:25</a></i>
;<br/> <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>hence </b><a NAME="E3:5"/>
( <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="realset2.html#K5" title="REALSET2:func.5">revf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">d</font></span>)</span> iff <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="realset2.html#K4" title="REALSET2:func.4">omf</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font> )
 <b>by </b><i><a class="txt" href="realset3.html#E1:5"><i><font color="Green" title="E6">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>
