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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#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-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="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>  st <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Olive" title="b1">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  holds <br/><font color="Olive" title="b1">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K14" title="SUBSTUT1:func.14">ExpandSub</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Olive" title="b1">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Olive" title="b2">xSQ</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="substut1.html#K38" title="SUBSTUT1:func.38">CQC-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="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>  st <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  holds <br/><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K14" title="SUBSTUT1:func.14">ExpandSub</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Olive" title="b1">xSQ</font></span>)</span></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="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> is  <a href="substut1.html#V3" title="SUBSTUT1:attr.3">quantifiable</a>  implies <font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K14" title="SUBSTUT1:func.14">ExpandSub</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span>)</span> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">Z</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">q</font> =  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:58"/>
<span class="p1"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</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"> <font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K14" title="SUBSTUT1:func.14">ExpandSub</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span>)</span></span><br/>

<a NAME="E2:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<span class="p1">(<span class="default"><span class="p2"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="substut1.html#K15" title="SUBSTUT1:func.15">QSub</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <span class="p3">(<span class="default"><span class="p4"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#D23" title="SUBSTUT1:def.23">SUBSTUT1:def 23</a></span>;<br/>
<a NAME="E3:58"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <span class="p3">(<span class="default"><span class="p4"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></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="E4:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <span class="p3">(<span class="default"><span class="p4"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="substut1.html#K23" title="SUBSTUT1:func.23">`2</a> </span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span>)</span> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></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="E5:58"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="qc_lang1.html#K8" title="QC_LANG1:func.8">QC-WFF</a> ,<a href="substut1.html#K1" title="SUBSTUT1:func.1">vSUB</a> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<a NAME="E6:58"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="sublemma.html#K8" title="SUBLEMMA:func.8">[</a><span class="default"><font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c1">x</font></span><a href="sublemma.html#K8" title="SUBLEMMA:func.8">]</a></span> <a href="sublemma.html#K9" title="SUBLEMMA:func.9">`1</a> </span>)</span> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K15" title="SUBSTUT1:func.15">QSub</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="txt" href="#E4:58"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="sublemma.html#T35" target="_self" title="SUBLEMMA:th.35">Th35</a>, <a class="ref" href="funct_1.html#T8" title="FUNCT_1:th.8">FUNCT_1:8</a></span>;<br/>
<a NAME="E7:58"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="substut1.html#K15" title="SUBSTUT1:func.15">QSub</a> 
 
<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/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">p</font> being   <a href="qc_lang1.html#NM8" title="QC_LANG1:NM.8">QC-formula</a>, <font color="Maroon" title="c7">Sub1</font> being   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a>, <font color="Maroon" title="c8">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E9:58"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">Sub1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c8">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E10:58"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">Sub1</font> <a href="substut1.html#R1" title="SUBSTUT1:pred.1">PQSub</a> <font color="Maroon" title="c8">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#D15" title="SUBSTUT1:def.15">SUBSTUT1:def 15</a></span>;<br/>
<a NAME="E11:58"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">Sub1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:58"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E12:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A5</font></span>: 
(  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p</font> &amp; <font color="Maroon" title="c3">xSQ</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">Sub1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E13:58"/><span class="lab"><font color="Green" title="E47">A6</font></span>: 
 <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span> is  <a href="qc_lang1.html#V5" title="QC_LANG1:attr.5">universal</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D20" title="QC_LANG1:def.20">QC_LANG1:def 20</a></span>;<br/>
<a NAME="E14:58"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A7</font></span>: 
 <a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="qc_lang1.html#D26" title="QC_LANG1:def.26">QC_LANG1:def 26</a></span>;<br/>
<a NAME="E15:58"/>
<font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:58"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E16:58"/><span class="kw">then </span>
<font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K14" title="SUBSTUT1:func.14">ExpandSub</a> <span class="p1">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <span class="p2">(<span class="default"><a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <span class="p3">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:58"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="txt" href="#E12:58"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="txt" href="#E13:58"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="ref" href="substut1.html#D14" title="SUBSTUT1:def.14">SUBSTUT1:def 14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:58"/>
<font color="Maroon" title="c2">S</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K14" title="SUBSTUT1:func.14">ExpandSub</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span>,<span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="sublemma.html#K2" title="SUBLEMMA:func.2">`1</a> </span>)</span></span>)</span>,<font color="Maroon" title="c3">xSQ</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:58"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="txt" href="#E14:58"><span class="lab"><font color="Green" title="E48">A7</font></span></a>, <a class="ref" href="qc_lang1.html#D27" title="QC_LANG1:def.27">QC_LANG1:def 27</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/>


</div>
