<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">IT</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2" target="_self">bound_QC-variables</a> , <font color="Maroon">IT'</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="qc_lang1.html#K2" target="_self">bound_QC-variables</a> ;<br/>

<b>given </b><font color="Maroon">F1</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> , <a href="zfmisc_1.html#K1">bool</a> <a href="qc_lang1.html#K2" target="_self">bound_QC-variables</a> <b> such that </b><a NAME="E1:48_1_2"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E2:48_1_2"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a>  holds <br/> ( <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <a href="qc_lang1.html#K11" target="_self">VERUM</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V2" target="_self">atomic</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K16" target="_self">the_arguments_of</a> <font color="Olive">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K16" target="_self">the_arguments_of</a> <font color="Olive">p</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="qc_lang1.html#K16" target="_self">the_arguments_of</a> <font color="Olive">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2" target="_self">bound_QC-variables</a>  ) </span>}</span>  ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V3" target="_self">negative</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" target="_self">the_argument_of</a> <font color="Olive">p</font></span>)</span> ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V4" target="_self">conjunctive</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K18" target="_self">the_left_argument_of</a> <font color="Olive">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19" target="_self">the_right_argument_of</a> <font color="Olive">p</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V5" target="_self">universal</a> implies <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21" target="_self">the_scope_of</a> <font color="Olive">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K20" target="_self">bound_in</a> <font color="Olive">p</font></span>)</span></span><a href="tarski.html#K1">}</a></span> ) )
 ;<br/>

<b>given </b><font color="Maroon">F2</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> , <a href="zfmisc_1.html#K1">bool</a> <a href="qc_lang1.html#K2" target="_self">bound_QC-variables</a> <b> such that </b><a NAME="E3:48_1_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">IT'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E4:48_1_2"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a>  holds <br/> ( <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <a href="qc_lang1.html#K11" target="_self">VERUM</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V2" target="_self">atomic</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="qc_lang1.html#K16" target="_self">the_arguments_of</a> <font color="Olive">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font></span>)</span> where <font color="Olive">k</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K16" target="_self">the_arguments_of</a> <font color="Olive">p</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="qc_lang1.html#K16" target="_self">the_arguments_of</a> <font color="Olive">p</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2" target="_self">bound_QC-variables</a>  ) </span>}</span>  ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V3" target="_self">negative</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K17" target="_self">the_argument_of</a> <font color="Olive">p</font></span>)</span> ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V4" target="_self">conjunctive</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K18" target="_self">the_left_argument_of</a> <font color="Olive">p</font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K19" target="_self">the_right_argument_of</a> <font color="Olive">p</font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">p</font> is <a href="qc_lang1.html#V5" target="_self">universal</a> implies <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K21" target="_self">the_scope_of</a> <font color="Olive">p</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K20" target="_self">bound_in</a> <font color="Olive">p</font></span>)</span></span><a href="tarski.html#K1">}</a></span> ) )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> ] <b>means </b><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<a NAME="E5:48_1_2"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">P</font> being  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">k</font><br/> for <font color="Olive">ll</font> being   <a href="qc_lang1.html#M1" target="_self">QC-variable_list</a> of <font color="Olive">k</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">P</font> <a href="qc_lang1.html#K9" target="_self">!</a> <font color="Olive">ll</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">P</font> be   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">k</font>;<br/><b>let </b><font color="Maroon">ll</font> be    <a href="qc_lang1.html#M1" target="_self">QC-variable_list</a> of <font color="Maroon">k</font>;<br/>





<a NAME="E1:48_1_2_1"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">P</font> <a href="qc_lang1.html#K9" target="_self">!</a> <font color="Maroon">ll</font> is <a href="qc_lang1.html#V2" target="_self">atomic</a>
 
<b>by </b><i/>;<br/>
<a NAME="E2:48_1_2_1"/><b>then </b><i><font color="Green">E59</font></i>: 
 <a href="qc_lang1.html#K16" target="_self">the_arguments_of</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="qc_lang1.html#K9" target="_self">!</a> <font color="Maroon">ll</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">ll</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="qc_lang1.html#K9" target="_self">!</a> <font color="Maroon">ll</font></span>)</span> = 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font></span>)</span> where <font color="Olive">j</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">j</font> &amp; <font color="Olive">j</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">ll</font> &amp; <font color="Maroon">ll</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2" target="_self">bound_QC-variables</a>  ) </span>}</span> 
<b>by </b><i>, <a class="txt" href="qc_lang1.html#E4:48_1_2"><i><font color="Green">E42</font></i></a></i>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="qc_lang1.html#K9" target="_self">!</a> <font color="Maroon">ll</font></span>)</span>
<b>by </b><i>, <a class="txt" href="qc_lang1.html#E4:48_1_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="qc_lang1.html#E5:48_1_2"><i><font color="Green">E43</font></i></a></i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E6:48_1_2"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="qc_lang1.html#K11" target="_self">VERUM</a> ]
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:48_1_2"/><i><font color="Green">E61</font></i>: 
for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="qc_lang1.html#K12" target="_self">'not'</a> <font color="Olive">p</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:48_1_2_2"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E2:48_1_2_2"/><i><font color="Green">E63</font></i>: 
 <a href="qc_lang1.html#K12" target="_self">'not'</a> <font color="Maroon">p</font> is <a href="qc_lang1.html#V3" target="_self">negative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:48_1_2_2"/><b>then </b><i><font color="Green">E64</font></i>: 
 <a href="qc_lang1.html#K17" target="_self">the_argument_of</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" target="_self">'not'</a> <font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" target="_self">'not'</a> <font color="Maroon">p</font></span>)</span> = 
<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>
<b>by </b><i>, <a class="ref" href="qc_lang1.html#D8" target="_self">Def8</a>, </i>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K12" target="_self">'not'</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="qc_lang1.html#D9" target="_self">Def9</a></i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E8:48_1_2"/><i><font color="Green">E65</font></i>: 
for <font color="Olive">p</font>, <font color="Olive">q</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">q</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Olive">q</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> , <font color="Maroon">q</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:48_1_2_3"/><i><font color="Green">E66</font></i>: 
( <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> &amp; <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">q</font> )
 ;<br/>

<a NAME="E2:48_1_2_3"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">p</font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Maroon">q</font> is <a href="qc_lang1.html#V4" target="_self">conjunctive</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:48_1_2_3"/><b>then </b><i><font color="Green">E93</font></i>: 
(  <a href="qc_lang1.html#K18" target="_self">the_left_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp;  <a href="qc_lang1.html#K19" target="_self">the_right_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> )
 
<b>by </b><i>, <a class="ref" href="qc_lang1.html#T4" target="_self">Th4</a></i>;<br/>
<b>hence </b><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">q</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="qc_lang1.html#D9" target="_self">Def9</a></i>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="qc_lang1.html#K13" target="_self">'&amp;'</a> <font color="Maroon">q</font></span>)</span>
<b>by </b><i>, <a class="ref" href="qc_lang1.html#D9" target="_self">Def9</a>, </i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E9:48_1_2"/><i><font color="Green">E94</font></i>: 
for <font color="Olive">x</font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a><br/> for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="qc_lang1.html#K14" target="_self">All</a> <font color="Olive">x</font>,<font color="Olive">p</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_2_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:48_1_2_4"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E2:48_1_2_4"/><i><font color="Green">E96</font></i>: 
 <a href="qc_lang1.html#K14" target="_self">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font> is <a href="qc_lang1.html#V5" target="_self">universal</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:48_1_2_4"/><b>then </b><i><font color="Green">E97</font></i>: 
(  <a href="qc_lang1.html#K21" target="_self">the_scope_of</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" target="_self">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp;  <a href="qc_lang1.html#K20" target="_self">bound_in</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" target="_self">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i><a class="ref" href="qc_lang1.html#T10" target="_self">Th10</a>, </i>;<br/>
<b>hence </b><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" target="_self">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, <a class="ref" href="qc_lang1.html#D9" target="_self">Def9</a>, </i>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K14" target="_self">All</a> <font color="Maroon">x</font>,<font color="Maroon">p</font></span>)</span>
<b>by </b><i>, , </i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E10:48_1_2"/>
for <font color="Olive">p</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="qc_lang1.html#K8" target="_self">QC-WFF</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">p</font>]
 
<b>from </b><i><a class="ref" href="qc_lang1.html#S1" target="_self">QC_LANG1:sch 1</a>(, <a class="txt" href="qc_lang1.html#E4:48_1_2"><i><font color="Green">E42</font></i></a>, <a class="txt" href="qc_lang1.html#E5:48_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="qc_lang1.html#D8" target="_self">Def8</a>, );<br/></i>
<b>hence </b><a NAME="E11:48_1_2"/>
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT'</font>
 <b>by </b><i>, </i>;<br/>


</div>
