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<span class="kw">let </span><font color="Maroon" title="c1">k</font>, <font color="Maroon" title="c2">n</font>, <font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">l</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c1">k</font></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> is   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c5">Y</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c1">k</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_5.html#T5" target="_self" onmouseover="rs('nat_5/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">X</font> = <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">m</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_5.html#T5" target="_self" onmouseover="rs('nat_5/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<a NAME="E3:7"/>
<span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c1">k</font></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c5">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T5" onmouseover="rs('enumset1/T5')" onmouseout="rh()">ENUMSET1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:7"/>
<span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default"><font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">l</font>,<font color="Maroon" title="c1">k</font></span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> is   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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