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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font>  ex <font color="Olive" title="b2">B</font> being   <a href="matroid0.html#M1" title="MATROID0:mode.1">Basis</a> of <font color="Maroon" title="c1">M</font> st <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a> <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">B</font> being   <a href="matroid0.html#M1" title="MATROID0:mode.1">Basis</a> of <font color="Maroon" title="c1">M</font> st <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B</font></span><br/>



<b>consider </b><font color="Maroon" title="c3">B</font> being  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font><b> such that </b><br/><a NAME="E2:58"/><i><font color="Green" title="E27">A1</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c3">B</font> <a href="matroid0.html#R1" title="MATROID0:pred.1">is_maximal_independent_in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">M</font> )
 <b>by </b><i><a class="ref" href="matroid0.html#T14" target="_self" title="MATROID0:th.14">Th</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">B</font> = <font color="Maroon" title="c3">B</font> as    <a href="matroid0.html#M1" title="MATROID0:mode.1">Basis</a> of <font color="Maroon" title="c1">M</font> <b>by </b><i><a class="txt" href="#E2:58"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="matroid0.html#D13" target="_self" title="MATROID0:def.13">BASIS</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">B</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font></span><br/>

<b>thus </b><a NAME="E4:58"/>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">B</font>
 <b>by </b><i><a class="txt" href="#E2:58"><i><font color="Green" title="E27">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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