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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="substut1.html#M1">second_Q_comp</a> of <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>assume </b><a NAME="E1:52"/><i><font color="Green">E39</font></i>: 
<span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span> is <a href="substut1.html#V3">quantifiable</a>
 ;<br/>

<a NAME="E2:52"/><b>then </b>
 <a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K24">Sub_All</a> <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="sublemma.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E3:52"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>3</sub></font> is <a href="substut1.html#V7">Sub_universal</a>
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:52"><i><font color="Green">E39</font></i></a>, <a class="ref" href="substut1.html#T14">SUBSTUT1:14</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>5</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">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>6</sub></font> being    <a href="substut1.html#M1">second_Q_comp</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E5:52"/><i><font color="Green">E41</font></i>: 
(  <a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K24">Sub_All</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="substut1.html#K23">`2</a>  <a href="hidden.html#R1">=</a>  <a href="substut1.html#K30">Sub_the_bound_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="substut1.html#V3">quantifiable</a> )
 <b>by </b><i><a class="txt" href="sublemma.html#E3:52"><i><font color="Green">E40</font></i></a>, <a class="ref" href="substut1.html#D33">SUBSTUT1:def 33</a></i>;<br/>
<a NAME="E6:52"/>
<span class="p1"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span> <a href="substut1.html#K23">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="substut1.html#K23">`2</a> 
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:52"><i><font color="Green">E39</font></i></a>, <a class="txt" href="sublemma.html#E5:52"><i><font color="Green">E41</font></i></a>, <a class="ref" href="sublemma.html#T37" target="_self">Th37</a></i>;<br/>
<b>hence </b><a NAME="E7:52"/>
 <a href="substut1.html#K30">Sub_the_bound_of</a> <span class="p1">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p2"><a href="sublemma.html#K8" target="_self">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="sublemma.html#K8" target="_self">]</a></span>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E5:52"><i><font color="Green">E41</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>


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