<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:21"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D6">XBOOLE_0:def 6</a>, <a class="ref" href="xboole_1.html#T51">XBOOLE_1:51</a>, <a class="ref" href="xboole_1.html#T82">XBOOLE_1:82</a>, <a class="ref" href="xboole_1.html#T89">XBOOLE_1:89</a></i>;<br/>
<a NAME="E2:21"/><b>then </b>
( not <!--HUMANRECFAILED-->( (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) &amp; (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) &amp; not  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> is <a href="abian.html#V1">even</a> ) &amp; (  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> is <a href="abian.html#V1">even</a> implies (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> iff  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) ) &amp; not <!--HUMANRECFAILED-->( (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) &amp; (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) &amp; not  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font> is <a href="abian.html#V1">even</a> ) &amp; (  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font> is <a href="abian.html#V1">even</a> implies (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="abian.html#V1">even</a> iff  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) ) &amp; not <!--HUMANRECFAILED-->( (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) &amp; (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) &amp; not  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) &amp; (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies (  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> iff  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) ) )
 
<b>by </b><i><a class="ref" href="chain_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E3:21"/>
( (  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> is <a href="abian.html#V1">even</a> iff  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font> is <a href="abian.html#V1">even</a> ) iff  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="abian.html#V1">even</a> )
 ;<br/>


</div>
