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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: MATROID0:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font> being   <a href="taxonom2.html#V4" title="TAXONOM2:attr.4">mutually-disjoint</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="matroid0.html#K2" title="MATROID0:func.2">ProdMatroid</a> <font color="Olive" title="b1">P</font></span>)</span><br/>  for <font color="Olive" title="b3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">P</font>  st (  for <font color="Olive" title="b4">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">x</font> holds <br/><font color="Olive" title="b4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">a</font> ) holds <br/>( <font color="Olive" title="b2">x</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">independent</a>  iff <font color="Olive" title="b3">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  )</div></div>
