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

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <font color="Maroon" title="c1">F</font> holds  <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_1.html#K1" title="FUNCT_1:func.1">.</a> <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="Olive" title="b1">a</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="Olive" title="b2">b</font></span>)</span></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">b</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">a</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <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_1.html#K1" title="FUNCT_1:func.1">.</a> <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="c2">a</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="c3">b</font></span>)</span></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">b</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="c2">a</font></span>)</span></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c4">revfa</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="c2">a</font>, <font color="Maroon" title="c5">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="c3">b</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <font color="Maroon" title="c1">F</font> ;<br/>
<a NAME="E2:4"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<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="c3">b</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="realset2.html#T28" title="REALSET2:th.28">REALSET2:28</a></span>;<br/>
<a NAME="E3:4"/><span class="lab"><font color="Green" title="E4">A2</font></span>: 
<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">b</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="c2">a</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="realset2.html#T28" title="REALSET2:th.28">REALSET2:28</a></span>;<br/>
<font color="Maroon" title="c5">revfb</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c4">revfa</font></span>)</span> = 
<font color="Maroon" title="c4">revfa</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">revfb</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="realset2.html#T8" title="REALSET2:th.8">REALSET2:8</a></span>
<br/>.= 
<font color="Maroon" title="c4">revfa</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <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">b</font>,<font color="Maroon" title="c5">revfb</font></span>)</span>

<br/>.= 
<font color="Maroon" title="c4">revfa</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="realset2.html#D18" title="REALSET2:def.18">REALSET2:def 18</a></span>
<br/>.= 
<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="c2">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="realset2.html#T10" title="REALSET2:th.10">REALSET2:10</a></span>
;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">revfb</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c4">revfa</font></span>)</span> = 
<font color="Maroon" title="c2">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c4">revfa</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="realset2.html#T8" title="REALSET2:th.8">REALSET2:8</a></span>
<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>,<font color="Maroon" title="c4">revfa</font>

<br/>.= 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c1">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="realset2.html#D18" title="REALSET2:def.18">REALSET2:def 18</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:4"/>
<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_1.html#K1" title="FUNCT_1:func.1">.</a> <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="c2">a</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="c3">b</font></span>)</span></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">b</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="c2">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:4"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="txt" href="#E3:4"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="realset2.html#T26" title="REALSET2:th.26">REALSET2:26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
