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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="card_3.html#NM1" title="CARD_3:NM.1">Cardinal-Function</a>;<br/>

<b>thus </b><a NAME="E1:41"/>
(  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> implies  <a href="card_3.html#K7" title="CARD_3:func.7">Product</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 <b>by </b><i><a class="ref" href="card_3.html#T37" target="_self" title="CARD_3:th.37">Th37</a>, <a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a></i>;<br/>

<b>assume </b><a NAME="E2:41"/>
 <a href="card_3.html#K7" title="CARD_3:func.7">Product</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/>

<a NAME="E3:41"/><b>then </b>
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">F</font>, <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="wellord2.html#R2" title="WELLORD2:pred.2">are_equipotent</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a>, <a class="ref" href="card_1.html#T21" title="CARD_1:th.21">CARD_1:21</a></i>;<br/>
<a NAME="E4:41"/><b>then </b>
 <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T46" title="CARD_1:th.46">CARD_1:46</a></i>;<br/>
<b>hence </b><a NAME="E5:41"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font>
 <b>by </b><i><a class="ref" href="card_3.html#T37" target="_self" title="CARD_3:th.37">Th37</a></i>;<br/>


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