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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="card_3.html#NM1">Cardinal-Function</a>;<br/>

<a NAME="E1:41"/><i><font color="Green">E24</font></i>: 
(  <a href="card_3.html#K7" target="_self">Product</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" target="_self">product</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="card_1.html#K1">Card</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="card_1.html#T47">CARD_1:47</a></i>;<br/>
<b>hence </b><a NAME="E2:41"/>
(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font> implies  <a href="card_3.html#K7" target="_self">Product</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="card_3.html#T37" target="_self">Th37</a></i>;<br/>

<b>assume </b><a NAME="E3:41"/>
 <a href="card_3.html#K7" target="_self">Product</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E4:41"/><b>then </b>
 <a href="card_3.html#K4" target="_self">product</a> <font color="Maroon">c<sub>1</sub></font>, <a href="xboole_0.html#K1">{}</a>  <a href="wellord2.html#R2">are_equipotent</a> 
 
<b>by </b><i><a class="txt" href="card_3.html#E1:41"><i><font color="Green">E24</font></i></a>, <a class="ref" href="card_1.html#T21">CARD_1:21</a></i>;<br/>
<a NAME="E5:41"/><b>then </b>
 <a href="card_3.html#K4" target="_self">product</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_1.html#T46">CARD_1:46</a></i>;<br/>
<b>hence </b><a NAME="E6:41"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="card_3.html#T37" target="_self">Th37</a></i>;<br/>


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