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<b>let </b><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font> be   <a href="card_3.html#NM1" title="CARD_3:NM.1">Cardinal-Function</a>;<br/>



<b>assume </b><a NAME="E1:42"/>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">G</font> &amp; ( for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> ) )
 ;<br/>

<a NAME="E2:42"/><b>then </b>
(  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K7" title="CARD_3:func.7">Product</a> <font color="Maroon" title="c2">G</font> &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K7" title="CARD_3:func.7">Product</a> <font color="Maroon" title="c1">F</font> &amp;  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c1">F</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <font color="Maroon" title="c2">G</font> )
 
<b>by </b><i><a class="ref" href="card_3.html#T38" target="_self" title="CARD_3:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E3:42"/>
 <a href="card_3.html#K7" title="CARD_3:func.7">Product</a> <font color="Maroon" title="c1">F</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a>  <a href="card_3.html#K7" title="CARD_3:func.7">Product</a> <font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a></i>;<br/>


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