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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">B1</font>, <font color="Olive" title="b2">B2</font> being   <a href="matroid0.html#M1" title="MATROID0:mode.1">Basis</a> of <font color="Maroon" title="c1">M</font> holds   <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b2">B2</font></span><br/><b>let </b><font color="Maroon" title="c2">B1</font>, <font color="Maroon" title="c3">B2</font> be    <a href="matroid0.html#M1" title="MATROID0:mode.1">Basis</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">  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">B2</font></span><br/>



<a NAME="E1:57"/>
( <font color="Maroon" title="c2">B1</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> &amp; <font color="Maroon" title="c3">B2</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#D13" target="_self" title="MATROID0:def.13">BASIS</a></i>;<br/>
<b>hence </b><a NAME="E2:57"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c3">B2</font>
 <b>by </b><i><a class="ref" href="matroid0.html#T16" target="_self" title="MATROID0:th.16">M3</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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