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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>   st  <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c1">X</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> holds <br/> <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a></span><br/><b>let </b><font color="Maroon" title="c2">p</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c1">X</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> implies  <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> )</span><br/>



<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E41">A1</font></i>: 
 <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c1">X</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a></span><br/>

<a NAME="E2:41"/>
 <a href="qc_lang1.html#K23" title="QC_LANG1:func.23">still_not-bound_in</a> <font color="Maroon" title="c2">p</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="cqc_sim1.html#T20" title="CQC_SIM1:th.20">CQC_SIM1:20</a></i>;<br/>
<a NAME="E3:41"/><b>then </b>
 <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="ref" href="goedelcp.html#T26" target="_self" title="GOEDELCP:th.26">Th26</a></i>;<br/>
<a NAME="E4:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
<b>by </b><i><a class="txt" href="#E1:41"><i><font color="Green" title="E41">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:41"/>
 <a href="goedelcp.html#K6" title="GOEDELCP:func.6">still_not-bound_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="ref" href="goedelcp.html#T27" target="_self" title="GOEDELCP:th.27">Th27</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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