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<b>let </b><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="catalan2.html#K1" title="CATALAN2:func.1">--&gt;</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="catalan2.html#K1" title="CATALAN2:func.1">--&gt;</a> <font color="Maroon" title="c3">k</font> )</span><br/>





<b>assume </b><a NAME="E1:10"/>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="catalan2.html#K1" title="CATALAN2:func.1">--&gt;</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="catalan2.html#K1" title="CATALAN2:func.1">--&gt;</a> <font color="Maroon" title="c3">k</font></span><br/>

<a NAME="E2:10"/><b>then </b>
<font color="Maroon" title="c1">n</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">m</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T40" title="NAT_1:th.40">NAT_1:40</a></i>;<br/>
<a NAME="E3:10"/><b>then </b>
<font color="Maroon" title="c1">n</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>;<br/>
<b>hence </b><a NAME="E4:10"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="catalan2.html#K1" title="CATALAN2:func.1">--&gt;</a> <font color="Maroon" title="c3">k</font></span>)</span> <a href="card_fin.html#K4" title="CARD_FIN:func.4">|</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="catalan2.html#K1" title="CATALAN2:func.1">--&gt;</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="ref" href="funcop_1.html#T18" title="FUNCOP_1:th.18">FUNCOP_1:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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