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

<b>set </b><font color="Maroon" title="c3">X</font> = <span class="p1">(<span class="default"><a href="substut1.html#K10" title="SUBSTUT1:func.10">Dom_Bound_Vars</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="substut1.html#K11" title="SUBSTUT1:func.11">Sub_Var</a> <font color="Maroon" title="c2">finSub</font></span>)</span>;<br/>
<a NAME="E1:19_1_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="substut1.html#K10" title="SUBSTUT1:func.10">Dom_Bound_Vars</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="substut1.html#K11" title="SUBSTUT1:func.11">Sub_Var</a> <font color="Maroon" title="c2">finSub</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="card_3.html#T58" title="CARD_3:th.58">CARD_3:58</a></i>;<br/>
<b>hence </b><a NAME="E2:19_1_1"/>
<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="substut1.html#K10" title="SUBSTUT1:func.10">Dom_Bound_Vars</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="substut1.html#K11" title="SUBSTUT1:func.11">Sub_Var</a> <font color="Maroon" title="c2">finSub</font></span>)</span></span>)</span> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="ref" href="card_2.html#T4" title="CARD_2:th.4">CARD_2:4</a>, <a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
