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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> <br/> for <font color="Olive" title="b2">xSQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>  st  <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Olive" title="b1">S</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  &amp; <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  holds <br/> <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Olive" title="b2">xSQ</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">xSQ</font> being   <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>  st  <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c2">S</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  &amp; <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  holds <br/> <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Olive" title="b1">xSQ</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">xSQ</font> be    <a href="substut1.html#M1" title="SUBSTUT1:mode.1">second_Q_comp</a> of <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c2">S</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  &amp; <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  implies  <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a>  )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">S9</font> =  <a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:95"/><span class="lab"><font color="Green" title="E57">A1</font></span>: 
 <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c2">S</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> 
 <span class="kw">and </span><br/><a NAME="E2:95"/><span class="lab"><font color="Green" title="E58">A2</font></span>: 
<span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> </span><br/>

<a NAME="E3:95"/>
 <a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span> <a href="substut1.html#K22" title="SUBSTUT1:func.22">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:95"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="ref" href="substut1.html#T21" target="_self" title="SUBSTUT1:th.21">Th21</a></span>;<br/>
<a NAME="E4:95"/><span class="kw">then </span>
 <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p4"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="qc_lang1.html#K14" title="QC_LANG1:func.14">All</a> <span class="p1">(<span class="default"><a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p2">(<span class="default"><a href="substut1.html#K32" title="SUBSTUT1:func.32">@</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p4"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <font color="Maroon" title="c2">S</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<a NAME="E5:95"/><span class="kw">then </span>
 <a href="substut1.html#K36" title="SUBSTUT1:func.36">Quant</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p2">(<span class="default"><a href="substut1.html#K31" title="SUBSTUT1:func.31">Sub_the_scope_of</a> <span class="p3">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p4"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span></span>)</span></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E57">A1</font></span></a>, <a class="ref" href="cqc_lang.html#T23" title="CQC_LANG:th.23">CQC_LANG:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:95"/>
 <a href="substut1.html#K37" title="SUBSTUT1:func.37">CQC_Sub</a> <span class="p1">(<span class="default"><a href="substut1.html#K24" title="SUBSTUT1:func.24">Sub_All</a> <span class="p2"><a href="substut1.html#K25" title="SUBSTUT1:func.25">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="substut1.html#K25" title="SUBSTUT1:func.25">]</a></span>,<font color="Maroon" title="c3">xSQ</font></span>)</span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K4" title="CQC_LANG:func.4">CQC-WFF</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:95"><span class="lab"><font color="Green" title="E58">A2</font></span></a>, <a class="ref" href="substut1.html#T14" target="_self" title="SUBSTUT1:th.14">Th14</a>, <a class="ref" href="substut1.html#T32" target="_self" title="SUBSTUT1:th.32">Th32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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