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<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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9" title="PARSP_1:func.9">MPS</a> <font color="Maroon" title="c1">F</font></span>)</span>  st <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b1">b</font>,<font color="Olive" title="b4">d</font> holds <br/><font color="Olive" title="b3">a</font>,<font color="Olive" title="b1">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b3">a</font>,<font color="Olive" title="b2">c</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="parsp_1.html#K9" title="PARSP_1:func.9">MPS</a> <font color="Maroon" title="c1">F</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">d</font> implies <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">c</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 <span class="kw">and </span><br/><a NAME="E2:17"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">and </span><br/><a NAME="E3:17"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font>
 <span class="kw">and </span><br/><a NAME="E4:17"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c5">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">c</font></span><br/>

<span class="kw">assume </span><a NAME="E5:17"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
 not <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">i</font>, <font color="Maroon" title="c7">j</font>, <font color="Maroon" title="c8">k</font>, <font color="Maroon" title="c9">l</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span><span class="kw"> such that </span><br/><a NAME="E7:17"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
<span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Maroon" title="c6">i</font>,<font color="Maroon" title="c7">j</font>,<font color="Maroon" title="c8">k</font>,<font color="Maroon" title="c9">l</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E8:17"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
(  ex <font color="Olive" title="b1">L</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font> st <br/>( <font color="Olive" title="b1">L</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"><font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> &amp; <font color="Olive" title="b1">L</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"><font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> &amp; <font color="Olive" title="b1">L</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"><font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">l</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="parsp_2.html#T2" target="_self" title="PARSP_2:th.2">Th2</a></span>;<br/>
<a NAME="E9:17"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
( <font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">i</font> &amp; <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">j</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="mcart_1.html#T29" title="MCART_1:th.29">MCART_1:29</a></span>;<br/>
<a NAME="E10:17"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
( <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">k</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">l</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="mcart_1.html#T29" title="MCART_1:th.29">MCART_1:29</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">e</font>, <font color="Maroon" title="c11">f</font>, <font color="Maroon" title="c12">g</font>, <font color="Maroon" title="c13">h</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span><span class="kw"> such that </span><br/><a NAME="E12:17"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
<span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Maroon" title="c10">e</font>,<font color="Maroon" title="c11">f</font>,<font color="Maroon" title="c12">g</font>,<font color="Maroon" title="c13">h</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E13:17"/>
(  ex <font color="Olive" title="b1">K</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font> st <br/>( <font color="Olive" title="b1">K</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"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> &amp; <font color="Olive" title="b1">K</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"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> &amp; <font color="Olive" title="b1">K</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"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> ) or ( <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="parsp_2.html#T2" target="_self" title="PARSP_2:th.2">Th2</a></span>;<br/>
<a NAME="E14:17"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="mcart_1.html#T29" title="MCART_1:th.29">MCART_1:29</a></span>;<br/>
<a NAME="E15:17"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">h</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="mcart_1.html#T29" title="MCART_1:th.29">MCART_1:29</a></span>;<br/>
<a NAME="E16:17"/><span class="lab"><font color="Green" title="E30">A13</font></span>: 
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="mcart_1.html#T29" title="MCART_1:th.29">MCART_1:29</a></span>;<br/>
<a NAME="E17:17"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="mcart_1.html#T29" title="MCART_1:th.29">MCART_1:29</a></span>;<br/>
<a NAME="E18:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A15</font></span>: 
<span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c3">c</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Maroon" title="c10">e</font>,<font color="Maroon" title="c11">f</font>,<font color="Maroon" title="c10">e</font>,<font color="Maroon" title="c12">g</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="ref" href="mcart_1.html#T29" title="MCART_1:th.29">MCART_1:29</a></span>;<br/>
<a NAME="E19:17"/>
( <font color="Maroon" title="c11">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> &amp; <font color="Maroon" title="c12">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K4" title="DOMAIN_1:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span><a href="domain_1.html#K4" title="DOMAIN_1:func.4">]</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T44" title="MCART_1:th.44">MCART_1:44</a></span>;<br/>
<a NAME="E20:17"/><span class="kw">then </span>
( <font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  or <font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  or <font color="Maroon" title="c6">i</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">j</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="parsp_2.html#T3" target="_self" title="PARSP_2:th.3">Th3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">L</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font><span class="kw"> such that </span><br/><a NAME="E22:17"/><span class="lab"><font color="Green" title="E33">A16</font></span>: 
<font color="Maroon" title="c14">L</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"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E23:17"/><span class="lab"><font color="Green" title="E34">A17</font></span>: 
<font color="Maroon" title="c14">L</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"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span>
 <span class="kw">and </span><br/><a NAME="E24:17"/><span class="lab"><font color="Green" title="E35">A18</font></span>: 
<font color="Maroon" title="c14">L</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"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:17"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="txt" href="#E14:17"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E16:17"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E15:17"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E10:17"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="parsp_2.html#E2"><span class="lab"><font color="Green" title="E2">Lm2</font></span></a></span>;<br/>
<a NAME="E25:17"/>
<font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="parsp_2.html#T5" target="_self" title="PARSP_2:th.5">Th5</a></span>;<br/>
<a NAME="E26:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A19</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K6" title="MCART_1:func.6">`2</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:17"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="txt" href="parsp_2.html#E14"><span class="lab"><font color="Green" title="E14">Lm9</font></span></a></span>;<br/>
<a NAME="E27:17"/>
<font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="parsp_2.html#T5" target="_self" title="PARSP_2:th.5">Th5</a></span>;<br/>
<a NAME="E28:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A20</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K7" title="MCART_1:func.7">`3</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:17"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="txt" href="parsp_2.html#E14"><span class="lab"><font color="Green" title="E14">Lm9</font></span></a></span>;<br/>
<a NAME="E29:17"/>
<font color="Maroon" title="c13">h</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E12:17"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="parsp_2.html#T5" target="_self" title="PARSP_2:th.5">Th5</a></span>;<br/>
<a NAME="E30:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">g</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">e</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">f</font> <a href="mcart_1.html#K5" title="MCART_1:func.5">`1</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:17"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="txt" href="parsp_2.html#E14"><span class="lab"><font color="Green" title="E14">Lm9</font></span></a></span>;<br/>
<a NAME="E31:17"/><span class="kw">then </span>
( <font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> &amp; <font color="Maroon" title="c14">L</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E18:17"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E26:17"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E28:17"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="ref" href="parsp_2.html#T4" target="_self" title="PARSP_2:th.4">Th4</a></span>;<br/>
<a NAME="E32:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<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> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <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>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></span>;<br/>
<a NAME="E33:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T5" title="RLVECT_1:th.5">RLVECT_1:5</a></span>;<br/>
<a NAME="E34:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></span>;<br/>
<a NAME="E35:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c14">L</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T33" title="RLVECT_1:th.33">RLVECT_1:33</a></span>;<br/>
<a NAME="E36:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c14">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>;<br/>
<a NAME="E37:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c14">L</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c14">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>;<br/>
<a NAME="E38:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c14">L</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>;<br/>
<a NAME="E39:17"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T5" title="RLVECT_1:th.5">RLVECT_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E40:17"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="rlvect_1.html#T4" title="RLVECT_1:th.4">RLVECT_1:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
