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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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"> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="heyting3.html#K2" title="HEYTING3:func.2">PFArt</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">k</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="heyting3.html#K1" title="HEYTING3:func.1">SubstPoset</a> (<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>)</span>)</span></span><br/>

<a NAME="E1:46"/>
 <a href="substlat.html#K1" title="SUBSTLAT:func.1">SubstitutionSet</a> (<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="heyting3.html#K1" title="HEYTING3:func.1">SubstPoset</a> (<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substlat.html#D4" onmouseover="rs('substlat/D4')" onmouseout="rh()">SUBSTLAT:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:46"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="heyting3.html#K2" title="HEYTING3:func.2">PFArt</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">k</font>)</span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="heyting3.html#K1" title="HEYTING3:func.1">SubstPoset</a> (<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="heyting2.html#T2" onmouseover="rs('heyting2/T2')" onmouseout="rh()">HEYTING2:2</a></span>; <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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