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<span class="kw">set </span><font color="Maroon" title="c2">a</font> =  the    <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/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">a</font> =  the    <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> 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> <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#D2" title="PRE_TOPC:def.2">PRE_TOPC:def 2</a></span>;<br/>
<a NAME="E2:11_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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="ref" href="matroid0.html#T1" target="_self" title="MATROID0:th.1">Th1</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">b</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">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="matroid0.html#NV1" title="MATROID0:NV.1">independent</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:11_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="matroid0.html#NV1" title="MATROID0:NV.1">independent</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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