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<span class="kw">let </span><font color="Maroon" title="c1">M</font> be   <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</a>  <a href="matroid0.html#NM2" title="MATROID0:NM.2">Matroid</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font><br/> for <font color="Olive" title="b4">e</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>  st <font color="Olive" title="b1">A</font> is  <a href="matroid0.html#NV1" title="MATROID0:NV.1">independent</a>  &amp; <font color="Olive" title="b2">B</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a>  &amp; <font color="Olive" title="b3">C</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a>  &amp; <font color="Olive" title="b2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Olive" title="b3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds <br/><font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">C</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">e</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>  st <font color="Maroon" title="c2">A</font> is  <a href="matroid0.html#NV1" title="MATROID0:NV.1">independent</a>  &amp; <font color="Maroon" title="c3">B</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a>  &amp; <font color="Maroon" title="c4">C</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a>  &amp; <font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c4">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> holds <br/><font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">e</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">M</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is  <a href="matroid0.html#NV1" title="MATROID0:NV.1">independent</a>  &amp; <font color="Maroon" title="c3">B</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a>  &amp; <font color="Maroon" title="c4">C</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a>  &amp; <font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c4">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> implies <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:83"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
<font color="Maroon" title="c2">A</font> is  <a href="matroid0.html#NV1" title="MATROID0:NV.1">independent</a> 
 <span class="kw">and </span><br/><a NAME="E2:83"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
<font color="Maroon" title="c3">B</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a> 
 <span class="kw">and </span><br/><a NAME="E3:83"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
<font color="Maroon" title="c4">C</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a> 
 <span class="kw">and </span><br/><a NAME="E4:83"/><span class="lab"><font color="Green" title="E47">A4</font></span>: 
<font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">and </span><br/><a NAME="E5:83"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
<font color="Maroon" title="c4">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">C</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:83_1"/>
<font color="Maroon" title="c4">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:83_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">C</font> is  <a href="matroid0.html#NV1" title="MATROID0:NV.1">independent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="matroid0.html#T3" target="_self" title="MATROID0:th.3">Th3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:83_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="matroid0.html#D16" target="_self" title="MATROID0:def.16">Def16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">c</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E8:83"/><span class="lab"><font color="Green" title="E49">A6</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font>
 <span class="kw">and </span><br/><a NAME="E9:83"/><span class="lab"><font color="Green" title="E50">A7</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<a NAME="E10:83"/>
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:83"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E8:83"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="txt" href="#E9:83"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E11:83"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A8</font></span>: 
<font color="Maroon" title="c6">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:83_2"/>
<font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:83_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">B</font> is  <a href="matroid0.html#NV1" title="MATROID0:NV.1">independent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="matroid0.html#T3" target="_self" title="MATROID0:th.3">Th3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:83_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="matroid0.html#D16" target="_self" title="MATROID0:def.16">Def16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E14:83"/><span class="lab"><font color="Green" title="E52">A9</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">and </span><br/><a NAME="E15:83"/><span class="lab"><font color="Green" title="E53">A10</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<span class="kw">assume </span><a NAME="E16:83"/><span class="lab"><font color="Green" title="E54">A11</font></span>: 
<font color="Maroon" title="c3">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E17:83"/>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:83"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E14:83"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="txt" href="#E15:83"><span class="lab"><font color="Green" title="E53">A10</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E18:83"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E19:83"/><span class="kw">then </span>
<font color="Maroon" title="c5">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:83"><span class="lab"><font color="Green" title="E52">A9</font></span></a>, <a class="txt" href="#E8:83"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="txt" href="#E11:83"><span class="lab"><font color="Green" title="E51">A8</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">D</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font><span class="kw"> such that </span><br/><a NAME="E21:83"/><span class="lab"><font color="Green" title="E55">A12</font></span>: 
<font color="Maroon" title="c8">D</font> is  <a href="matroid0.html#V5" title="MATROID0:attr.5">cycle</a> 
 <span class="kw">and </span><br/><a NAME="E22:83"/><span class="lab"><font color="Green" title="E56">A13</font></span>: 
<font color="Maroon" title="c8">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="txt" href="#E3:83"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="txt" href="#E16:83"><span class="lab"><font color="Green" title="E54">A11</font></span></a>, <a class="ref" href="matroid0.html#T43" target="_self" title="MATROID0:th.43">Th43</a></span>;<br/>
<a NAME="E23:83"/>
<font color="Maroon" title="c8">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">D</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:83_3"/><span class="lab"><font color="Green" title="E57">A14</font></span>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font></span><br/>

<a NAME="E2:83_3"/><span class="kw">then </span>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c4">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:83"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E3:83_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A15</font></span>: 
( <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E4:83_3"/>
<font color="Maroon" title="c9">x</font> <a href="aofa_000.html#NR1" title="AOFA_000:NR.1">nin</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">e</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:83"><span class="lab"><font color="Green" title="E56">A13</font></span></a>, <a class="txt" href="#E1:83_3"><span class="lab"><font color="Green" title="E57">A14</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:83_3"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:83"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E5:83"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="txt" href="#E3:83_3"><span class="lab"><font color="Green" title="E58">A15</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E24:83"/><span class="kw">then </span>
<font color="Maroon" title="c8">D</font> is  <a href="matroid0.html#NV1" title="MATROID0:NV.1">independent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="matroid0.html#T3" target="_self" title="MATROID0:th.3">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:83"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:83"><span class="lab"><font color="Green" title="E55">A12</font></span></a>, <a class="ref" href="matroid0.html#D16" target="_self" title="MATROID0:def.16">Def16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
