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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="card_3.html#NM1">Cardinal-Function</a>;<br/>



<b>assume </b><a NAME="E1:43"/>
<font color="Maroon">c<sub>1</sub></font> <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:43"/><b>then </b>
 <a href="card_3.html#K2" target="_self">disjoin</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_4.html#NR1" target="_self">&lt;=</a>  <a href="card_3.html#K2" target="_self">disjoin</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="card_3.html#T34" target="_self">Th34</a></i>;<br/>
<a NAME="E3:43"/><b>then </b>
(  <a href="card_3.html#K3" target="_self">Union</a> <span class="p1">(<span class="default"><a href="card_3.html#K2" target="_self">disjoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="card_3.html#K3" target="_self">Union</a> <span class="p1">(<span class="default"><a href="card_3.html#K2" target="_self">disjoin</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="card_3.html#K6" target="_self">Sum</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#K3" target="_self">Union</a> <span class="p2">(<span class="default"><a href="card_3.html#K2" target="_self">disjoin</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp;  <a href="card_3.html#K6" target="_self">Sum</a> <font color="Maroon">c<sub>2</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#K3" target="_self">Union</a> <span class="p2">(<span class="default"><a href="card_3.html#K2" target="_self">disjoin</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="card_3.html#T35" target="_self">Th35</a></i>;<br/>
<b>hence </b><a NAME="E4:43"/>
 <a href="card_3.html#K6" target="_self">Sum</a> <font color="Maroon">c<sub>1</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_3.html#K6" target="_self">Sum</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="card_1.html#T27">CARD_1:27</a></i>;<br/>


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