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

<b>let </b><font color="Maroon">F</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/>

<a NAME="E1:16"/><i><font color="Green">E17</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9">MPS</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font></span><a href="zfmisc_1.html#K3">:]</a></span>
 
<b>by </b><i><a class="ref" href="parsp_1.html#T21">PARSP_1:21</a></i>;<br/>
<b>consider </b><font color="Maroon">e</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font></span><a href="zfmisc_1.html#K3">:]</a></span>, <font color="Maroon">f</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font></span><a href="zfmisc_1.html#K3">:]</a></span>, <font color="Maroon">g</font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font></span><a href="zfmisc_1.html#K3">:]</a></span><b> such that </b><br/><a NAME="E3:16"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span><a href="domain_1.html#K4">]</a></span> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span><a href="domain_1.html#K4">]</a></span> &amp; <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span><a href="domain_1.html#K4">]</a></span> )
 ;<br/>
<a NAME="E4:16"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">e</font> <a href="mcart_1.html#K5">`1</a>  <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> &amp; <font color="Maroon">e</font> <a href="mcart_1.html#K6">`2</a>  <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> &amp; <font color="Maroon">e</font> <a href="mcart_1.html#K7">`3</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> &amp; <font color="Maroon">f</font> <a href="mcart_1.html#K5">`1</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="mcart_1.html#K6">`2</a>  <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> &amp; <font color="Maroon">f</font> <a href="mcart_1.html#K7">`3</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> &amp; <font color="Maroon">g</font> <a href="mcart_1.html#K5">`1</a>  <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> &amp; <font color="Maroon">g</font> <a href="mcart_1.html#K6">`2</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span> &amp; <font color="Maroon">g</font> <a href="mcart_1.html#K7">`3</a>  <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> )
 
<b>by </b><i><a class="txt" href="parsp_2.html#E3:16"><i><font color="Green">E18</font></i></a>, <a class="ref" href="mcart_1.html#T47">MCART_1:47</a></i>;<br/>
<a NAME="E5:16"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<i><font color="Green">E47</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="parsp_2.html#T1" target="_self">Th1</a>, <a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T44">VECTSP_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>
;<br/>
<a NAME="E2:16_1"/>
 <a href="group_1.html#K2">1.</a> <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/>
<b>hence </b><a NAME="E3:16_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9">MPS</a> <font color="Maroon">F</font></span>)</span>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9">MPS</a> <font color="Maroon">F</font></span>)</span>, <font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9">MPS</a> <font color="Maroon">F</font></span>)</span><b> such that </b><br/><a NAME="E7:16"/><i><font color="Green">E48</font></i>: 
<span class="p1"><a href="domain_1.html#K5">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K5">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Maroon">e</font>,<font color="Maroon">f</font>,<font color="Maroon">e</font>,<font color="Maroon">g</font></span><a href="mcart_1.html#K4">]</a></span>
 <b>by </b><i><a class="txt" href="parsp_2.html#E1:16"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">a</font>
;<br/>

<b>take </b>
<font color="Maroon">b</font>
;<br/>

<b>take </b>
<font color="Maroon">c</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e'</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font></span><a href="zfmisc_1.html#K3">:]</a></span>, <font color="Maroon">f'</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font></span><a href="zfmisc_1.html#K3">:]</a></span>, <font color="Maroon">g'</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font></span><a href="zfmisc_1.html#K3">:]</a></span>, <font color="Maroon">h'</font> be    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F</font></span><a href="zfmisc_1.html#K3">:]</a></span>;<br/><b>assume </b><a NAME="E1:16_2"/>
<span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Maroon">e'</font>,<font color="Maroon">f'</font>,<font color="Maroon">g'</font>,<font color="Maroon">h'</font></span><a href="mcart_1.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K5">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K5">]</a></span>
 ;<br/><a NAME="E2:16_2"/><b>then </b>
( <font color="Maroon">e'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; <font color="Maroon">g'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">h'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> )
 <b>by </b><i>, <a class="ref" href="mcart_1.html#T33">MCART_1:33</a></i>;<br/><b>hence </b><a NAME="E3:16_2"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e'</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f'</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g'</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">h'</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g'</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">h'</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e'</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f'</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e'</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f'</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g'</font> <a href="mcart_1.html#K7">`3</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">h'</font> <a href="mcart_1.html#K7">`3</a> </span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g'</font> <a href="mcart_1.html#K5">`1</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">h'</font> <a href="mcart_1.html#K5">`1</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e'</font> <a href="mcart_1.html#K7">`3</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f'</font> <a href="mcart_1.html#K7">`3</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e'</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f'</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g'</font> <a href="mcart_1.html#K7">`3</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">h'</font> <a href="mcart_1.html#K7">`3</a> </span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g'</font> <a href="mcart_1.html#K6">`2</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">h'</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">e'</font> <a href="mcart_1.html#K7">`3</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">f'</font> <a href="mcart_1.html#K7">`3</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:16"/>
not <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_1.html#R1">'||'</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="parsp_1.html#T23">PARSP_1:23</a></i>;<br/>


</div>
