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<b>let </b><font color="Maroon">F</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9" target="_self">MPS</a> <font color="Maroon">F</font></span>)</span>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9" target="_self">MPS</a> <font color="Maroon">F</font></span>)</span>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9" target="_self">MPS</a> <font color="Maroon">F</font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:39"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">a</font>,<font color="Maroon">c</font>
 ;<br/>

<b>then 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>, <font color="Maroon">h</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="E3:39"/><i><font color="Green">E24</font></i>: 
<span class="p1"><a href="domain_1.html#K5">[</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="domain_1.html#K5">]</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>
 <b>and </b><br/><a NAME="E4:39"/><i><font color="Green">E33</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">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#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> &amp; <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#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> &amp; <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#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> )
 <b>by </b><i><a class="txt" href="parsp_1.html#E9"><i><font color="Green">Lemma28</font></i></a></i>;<br/>
<a NAME="E5:39"/>
( <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 
<b>by </b><i><a class="txt" href="parsp_1.html#E4:39"><i><font color="Green">E33</font></i></a>, <a class="ref" href="mcart_1.html#T33">MCART_1:33</a></i>;<br/>
<a NAME="E6:39"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K5">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">e</font>,<font color="Maroon">f</font>,<font color="Maroon">h</font></span><a href="domain_1.html#K5">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K5">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K5">]</a></span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</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">e</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">f</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">f</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">f</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">e</font> <a href="mcart_1.html#K6">`2</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</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">e</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">f</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">f</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">f</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">e</font> <a href="mcart_1.html#K7">`3</a> </span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</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">e</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">f</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">f</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">f</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">e</font> <a href="mcart_1.html#K7">`3</a> </span>)</span></span>)</span></span>)</span> <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_1.html#E14"><i><font color="Green">Lemma34</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E7:39"/>
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">b</font>,<font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="parsp_1.html#E9"><i><font color="Green">Lemma28</font></i></a></i>;<br/>


</div>
