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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">Y</font> implies ( (  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  iff  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">Y</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) iff  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:15"/>
<font color="Maroon" title="c1">X</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  iff  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">Y</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) iff  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  )</span><br/>

<a NAME="E2:15"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T40" title="CARD_2:th.40">CARD_2:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:15"/>
( (  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  iff  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">Y</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) iff  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y</font></span>)</span> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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