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<b>let </b><font color="Maroon" title="c1">p</font> be    <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> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="qc_lang1.html#NM3" title="QC_LANG1:NM.3">bound_QC-variable</a>;<br/><b>let </b><font color="Maroon" title="c3">Sub</font> be   <a href="substut1.html#NM1" title="SUBSTUT1:NM.1">CQC_Substitution</a>;<br/>





<b>set </b><font color="Maroon" title="c4">finSub</font> =  <a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">x</font>,<span class="p1">(<span class="default"><a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font>;<br/>
<b>set </b><font color="Maroon" title="c5">S</font> = <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2: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="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span>;<br/>
<b>assume </b><a NAME="E1:9"/><i><font color="Green" title="E9">A1</font></i>: 
not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><a href="substut1.html#K7" title="SUBSTUT1:func.7">RestrictSub</a> <font color="Maroon" title="c2">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="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span>)</span>
 ;<br/>

<a NAME="E2:9"/><i><font color="Green" title="E10">A2</font></i>: 
( <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2: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="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cqc_lang.html#K12" title="CQC_LANG:func.12">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c1">p</font> &amp; <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2: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="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> <a href="substut1.html#K34" title="SUBSTUT1:func.34">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Sub</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">q</font> = <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2: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="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> <a href="substut1.html#K33" title="SUBSTUT1:func.33">`1</a>  as    <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>  <b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<a NAME="E4:9"/>
(  <a href="qc_lang1.html#K20" title="QC_LANG1:func.20">bound_in</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="qc_lang1.html#K21" title="QC_LANG1:func.21">the_scope_of</a> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">p</font> )
 
<b>by </b><i><a class="txt" href="substut2.html#E2:9"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="qc_lang2.html#T8" title="QC_LANG2:th.8">QC_LANG2:8</a></i>;<br/>
<b>hence </b><a NAME="E5:9"/>
 <a href="substut1.html#K35" title="SUBSTUT1:func.35">S_Bound</a> <span class="p1"><a href="substut2.html#K1" title="SUBSTUT2: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="c2">x</font>,<font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">Sub</font></span><a href="substut2.html#K1" title="SUBSTUT2:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="substut2.html#E1:9"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="substut2.html#E2:9"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="substut1.html#D36" title="SUBSTUT1:def.36">SUBSTUT1:def 36</a></i>;<br/>


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