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<span class="kw">set </span><font color="Maroon" title="c4">Al2</font> =  <a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font>;<br/>
<a NAME="E1:5_1_1"/>
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <span class="p3">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"> { <span class="default"> <span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"> the    <a href="goedcpuc.html#M1" title="GOEDCPUC:mode.1">free_symbol</a> of <font color="Maroon" title="c1">Al</font>,<span class="p5"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">q</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>, <font color="Olive" title="b2">y</font> is   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font> : verum </span> } </span> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#T5" onmouseover="rs('qc_lang1/T5')" onmouseout="rh()">QC_LANG1:5</a></span>;<br/>
<a NAME="E2:5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E4">A1</font></span>: 
 <a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <span class="p1">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <font color="Maroon" title="c1">Al</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"> the    <a href="goedcpuc.html#M1" title="GOEDCPUC:mode.1">free_symbol</a> of <font color="Maroon" title="c1">Al</font>,<span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">q</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>, <font color="Olive" title="b2">y</font> is   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font> : verum </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T110" onmouseover="rs('zfmisc_1/T110')" onmouseout="rh()">ZFMISC_1:110</a></span>;<br/>
<a NAME="E3:5_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"> the    <a href="goedcpuc.html#M1" title="GOEDCPUC:mode.1">free_symbol</a> of <font color="Maroon" title="c1">Al</font>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"> the    <a href="goedcpuc.html#M1" title="GOEDCPUC:mode.1">free_symbol</a> of <font color="Maroon" title="c1">Al</font>,<span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">q</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">q</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a> <font color="Maroon" title="c1">Al</font>, <font color="Olive" title="b2">y</font> is   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <font color="Maroon" title="c1">Al</font> : verum </span> } </span> 
 
;<br/>
<a NAME="E4:5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A2</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"> the    <a href="goedcpuc.html#M1" title="GOEDCPUC:mode.1">free_symbol</a> of <font color="Maroon" title="c1">Al</font>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <span class="p1">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:5_1_1"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="xboole_0.html#D3" onmouseover="rs('xboole_0/D3')" onmouseout="rh()">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E5:5_1_1"/>
4 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">4</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E6:5_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">4,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"> the    <a href="goedcpuc.html#M1" title="GOEDCPUC:mode.1">free_symbol</a> of <font color="Maroon" title="c1">Al</font>,<span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">4</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K1" title="QC_LANG1:func.1">QC-symbols</a> <span class="p3">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:5_1_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:5_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">4,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"> the    <a href="goedcpuc.html#M1" title="GOEDCPUC:mode.1">free_symbol</a> of <font color="Maroon" title="c1">Al</font>,<span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">p</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> is   <a href="qc_lang1.html#NM5" title="QC_LANG1:NM.5">bound_QC-variable</a> of <span class="p1">(<span class="default"><a href="goedcpuc.html#K1" title="GOEDCPUC:func.1">FCEx</a> <font color="Maroon" title="c1">Al</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D4" onmouseover="rs('qc_lang1/D4')" onmouseout="rh()">QC_LANG1:def 4</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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