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<a NAME="E1:17"/>
 <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  is <a href="qc_lang1.html#V1" title="QC_LANG1:attr.1">QC-closed</a>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D10" title="QC_LANG1:def.10">QC_LANG1:def 10</a></i>;<br/>
<a NAME="E2:17"/><b>then </b><i><font color="Green" title="E17">A1</font></i>: 
 <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><span class="p2"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="qc_lang1.html#D9" title="QC_LANG1:def.9">QC_LANG1:def 9</a></i>;<br/>
<a NAME="E3:17"/>
<span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> is <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>
 
<b>by </b><i><a class="ref" href="card_4.html#T55" title="CARD_4:th.55">CARD_4:55</a></i>;<br/>
<a NAME="E4:17"/><b>then </b>
<span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  is <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>
 
<b>by </b><i><a class="ref" href="card_4.html#T65" title="CARD_4:th.65">CARD_4:65</a></i>;<br/>
<b>hence </b><a NAME="E5:17"/>
 <a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a>  is <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>
 <b>by </b><i><a class="txt" href="#E2:17"><i><font color="Green" title="E17">A1</font></i></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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