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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>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="substut1.html#K39">CQC_Sub</a> <span class="p1">(<span class="default"><a href="sublemma.html#K11" target="_self">CQCSub_the_scope_of</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><a NAME="E1:46"/><i><font color="Green">E36</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="E2:46"/><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="E3:46"/><b>then </b><i><font color="Green">E37</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#E1:46"><i><font color="Green">E36</font></i></a>, <a class="ref" href="substut1.html#T14">SUBSTUT1:14</a></i>;<br/>
<a NAME="E4:46"/><i><font color="Green">E38</font></i>: 
 <a href="sublemma.html#K12" target="_self">CQCQuant</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>,<span class="p1">(<span class="default"><a href="substut1.html#K39">CQC_Sub</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="sublemma.html#K12" target="_self">CQCQuant</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>,<span class="p1">(<span class="default"><a href="substut1.html#K39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" target="_self">CQCSub_the_scope_of</a> <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></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E1:46"><i><font color="Green">E36</font></i></a>, <a class="ref" href="sublemma.html#T31" target="_self">Th31</a></i>;<br/>
<a NAME="E5:46"/><i><font color="Green">E39</font></i>: 
 <a href="sublemma.html#K12" target="_self">CQCQuant</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>,<span class="p1">(<span class="default"><a href="substut1.html#K39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" target="_self">CQCSub_the_scope_of</a> <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></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K36">Quant</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>,<span class="p1">(<span class="default"><a href="substut1.html#K39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" target="_self">CQCSub_the_scope_of</a> <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></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E3:46"><i><font color="Green">E37</font></i></a>, <a class="ref" href="sublemma.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E6:46"/>
 <a href="substut1.html#K36">Quant</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>,<span class="p1">(<span class="default"><a href="substut1.html#K39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" target="_self">CQCSub_the_scope_of</a> <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></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K15">All</a> <span class="p1">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p2">(<span class="default"><a href="substut1.html#K32">@</a> <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></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K39">CQC_Sub</a> <span class="p2">(<span class="default"><a href="sublemma.html#K11" target="_self">CQCSub_the_scope_of</a> <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></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="substut1.html#D37">SUBSTUT1:def 37</a></i>;<br/>
<b>hence </b><a NAME="E7:46"/>
 <a href="sublemma.html#K12" target="_self">CQCQuant</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>,<span class="p1">(<span class="default"><a href="substut1.html#K39">CQC_Sub</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K15">All</a> <span class="p1">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p2">(<span class="default"><a href="substut1.html#K32">@</a> <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></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K39">CQC_Sub</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:46"><i><font color="Green">E36</font></i></a>, <a class="txt" href="sublemma.html#E4:46"><i><font color="Green">E38</font></i></a>, <a class="txt" href="sublemma.html#E5:46"><i><font color="Green">E39</font></i></a>, <a class="ref" href="sublemma.html#T31" target="_self">Th31</a></i>;<br/>


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