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<div class="add">

<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>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="substut1.html#K35">S_Bound</a> <span class="p1">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><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></span>)</span>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:68"/><i><font color="Green">E52</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>
 <b>and </b><br/><a NAME="E2:68"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>

<a NAME="E3:68"/>
 <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="txt" href="sublemma.html#E1:68"><i><font color="Green">E52</font></i></a>, <a class="ref" href="sublemma.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E4:68"/><b>then </b><i><font color="Green">E54</font></i>: 
( <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="sublemma.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K15">All</a> <span class="p1">(<span class="default"><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> <a href="substut1.html#K23">`2</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="sublemma.html#K9" target="_self">`1</a> </span>)</span> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span> &amp; <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="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:68"><i><font color="Green">E52</font></i></a>, <a class="ref" href="sublemma.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E5:68"/><b>then </b>
<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="sublemma.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="sublemma.html#K9" target="_self">`1</a> </span>)</span> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E6:68"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="qc_lang1.html#K20">bound_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="qc_lang2.html#T8">QC_LANG2:8</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="substut1.html#K7">RestrictSub</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p4"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><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="substut1.html#K19">`2</a> </span>)</span>;<br/>
<a NAME="E7:68"/><i><font color="Green">E56</font></i>: 
<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="sublemma.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="sublemma.html#K9" target="_self">`1</a> </span>)</span> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E4:68"><i><font color="Green">E54</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E8:68"/><b>then </b><i><font color="Green">E57</font></i>: 
<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="sublemma.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E9:68"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="qc_lang1.html#K20">bound_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E7:68"><i><font color="Green">E56</font></i></a>, <a class="ref" href="qc_lang2.html#T8">QC_LANG2:8</a></i>;<br/>
<a NAME="E10:68"/><i><font color="Green">E59</font></i>: 
 <a href="qc_lang1.html#K20">bound_in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p5"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p4"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p4"><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="substut1.html#K19">`2</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E2:68"><i><font color="Green">E53</font></i></a>, <a class="txt" href="sublemma.html#E4:68"><i><font color="Green">E54</font></i></a>, <a class="txt" href="sublemma.html#E6:68"><i><font color="Green">E55</font></i></a>, <a class="txt" href="sublemma.html#E7:68"><i><font color="Green">E56</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E11:68"/>
 <a href="substut1.html#K32">@</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>  <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>
 
<b>by </b><i><a class="ref" href="substut1.html#D35">SUBSTUT1:def 35</a></i>;<br/>
<a NAME="E12:68"/><b>then </b>
 <a href="substut1.html#K35">S_Bound</a> <span class="p1">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><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></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang3.html#K2">x.</a> <span class="p1">(<span class="default"><a href="substut1.html#K13">upVar</a> <span class="p2">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <span class="p3">(<span class="default"><a href="qc_lang1.html#K20">bound_in</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p0"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p5"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p5"><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="substut1.html#K19">`2</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="qc_lang1.html#K21">the_scope_of</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p5"><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="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E10:68"><i><font color="Green">E59</font></i></a>, <a class="ref" href="substut1.html#D36">SUBSTUT1:def 36</a></i>;<br/>
<b>hence </b><a NAME="E13:68"/>
 <a href="substut1.html#K35">S_Bound</a> <span class="p1">(<span class="default"><a href="substut1.html#K32">@</a> <span class="p2">(<span class="default"><a href="sublemma.html#K10" target="_self">CQCSub_All</a> <span class="p3"><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></span>)</span> <a href="hidden.html#R1">=</a>  <a href="qc_lang3.html#K2">x.</a> <span class="p1">(<span class="default"><a href="substut1.html#K13">upVar</a> <span class="p2">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E4:68"><i><font color="Green">E54</font></i></a>, <a class="txt" href="sublemma.html#E8:68"><i><font color="Green">E57</font></i></a>, <a class="txt" href="sublemma.html#E9:68"><i><font color="Green">E58</font></i></a>, <a class="ref" href="qc_lang2.html#T8">QC_LANG2:8</a></i>;<br/>


</div>
