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<b>let </b><font color="Maroon" title="c1">M</font> be   <a href="matroid0.html#NM1" title="MATROID0:NM.1">SubsetFamilyStr</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">M</font> is <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</a> implies <font color="Maroon" title="c1">M</font> is <a href="matroid0.html#V3" title="MATROID0:attr.3">finite-membered</a> )</span><br/>

<b>assume </b><a NAME="E1:22_1_1"/>
<font color="Maroon" title="c1">M</font> is <a href="matroid0.html#V3" title="MATROID0:attr.3">finite-membered</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="matroid0.html#D7" target="_self" title="MATROID0:def.7">MATROID0:def 7</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">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  ex <font color="Olive" title="b2">A</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font> st <br/>( <font color="Olive" title="b2">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a> &amp; not  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b2">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> ) or <font color="Maroon" title="c1">M</font> is <a href="matroid0.html#V3" title="MATROID0:attr.3">finite-membered</a> )</span><br/>

<b>hence </b><a NAME="E2:22_1_1"/>
( for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  ex <font color="Olive" title="b2">A</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">M</font> st <br/>( <font color="Olive" title="b2">A</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a> &amp; not  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b2">A</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> ) or <font color="Maroon" title="c1">M</font> is <a href="matroid0.html#V3" title="MATROID0:attr.3">finite-membered</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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