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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ;<br/>



<b>given </b><font color="Maroon">c<sub>4</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2">:]</a></span>, <font color="Maroon">c<sub>5</sub></font> being    <a href="substut1.html#M1" target="_self">second_Q_comp</a> of <font color="Maroon">c<sub>4</sub></font><b> such that </b><a NAME="E1:57_1_2"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K24" target="_self">Sub_All</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="substut1.html#V3" target="_self">quantifiable</a> )
 ;<br/>

<b>given </b><font color="Maroon">c<sub>6</sub></font> being    <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="substut1.html#K16" target="_self">QC-Sub-WFF</a> ,<a href="qc_lang1.html#K2">bound_QC-variables</a> </span><a href="zfmisc_1.html#K2">:]</a></span>, <font color="Maroon">c<sub>7</sub></font> being    <a href="substut1.html#M1" target="_self">second_Q_comp</a> of <font color="Maroon">c<sub>6</sub></font><b> such that </b><a NAME="E2:57_1_2"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K24" target="_self">Sub_All</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K22" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="substut1.html#V3" target="_self">quantifiable</a> )
 ;<br/>

<a NAME="E3:57_1_2"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i><a class="txt" href="substut1.html#E1:57_1_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="substut1.html#E2:57_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="substut1.html#D24" target="_self">Def24</a></i>;<br/>
<a NAME="E4:57_1_2"/><b>then </b>
(  <a href="qc_lang1.html#K14">All</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K14">All</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E5:57_1_2"/><b>then </b><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K23" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K23" target="_self">`2</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a>  )
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T6">QC_LANG2:6</a></i>;<br/>
<a NAME="E6:57_1_2"/><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K19" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <a href="substut1.html#K15" target="_self">QSub</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><a href="qc_lang1.html#K14">All</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K23" target="_self">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="txt" href="substut1.html#E1:57_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="substut1.html#D23" target="_self">Def23</a></i>;<br/>
<a NAME="E7:57_1_2"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K22" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K18" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K22" target="_self">`1</a> </span>)</span> <a href="substut1.html#K19" target="_self">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span> )
 
<b>by </b><i><a class="ref" href="substut1.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E8:57_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="substut1.html#E1:57_1_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="substut1.html#E2:57_1_2"><i><font color="Green">E33</font></i></a>, <a class="txt" href="substut1.html#E3:57_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="substut1.html#E5:57_1_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="substut1.html#E6:57_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="substut1.html#D23" target="_self">Def23</a></i>;<br/>


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