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<b>consider </b><font color="Maroon" title="c2">a</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">M</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">a</font> as  <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>by </b><i><a class="ref" href="pre_topc.html#D5" title="PRE_TOPC:def.5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E3:11_1_1"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">b</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as  <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>by </b><i><a class="ref" href="matroid0.html#T1" target="_self" title="MATROID0:th.1">Th2</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="c4">b</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Maroon" title="c4">b</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a> )</span><br/>

<b>thus </b><a NAME="E5:11_1_1"/>
( <font color="Maroon" title="c4">b</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> &amp; <font color="Maroon" title="c4">b</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a> )
 ; <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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