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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="qc_lang1.html#NM3">bound_QC-variable</a>;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="substut1.html#NM1">CQC_Substitution</a>ex <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a>  st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="substut1.html#NM1">CQC_Substitution</a>;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K15">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sublemma.html#K13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" target="_self">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K1" target="_self">]</a></span></span>)</span></span>)</span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="substut1.html#K2">@</a> <span class="p2">(<span class="default"><a href="substut1.html#K7">RestrictSub</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="sublemma.html#K15">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="sublemma.html#K13">|</a> <span class="p2">(<span class="default"><a href="substut1.html#K35">S_Bound</a> <span class="p3"><a href="substut2.html#K1" target="_self">[</a><span class="default"><span class="p4">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K1" target="_self">]</a></span></span>)</span></span>)</span> as   <a href="substut1.html#NM1">CQC_Substitution</a> <b>by </b><i><a class="ref" href="partfun1.html#T119">PARTFUN1:119</a>, <a class="ref" href="substut1.html#D1">SUBSTUT1:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> <b> such that </b><br/><a NAME="E4:12"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="substut2.html#E1:12"><i><font color="Green">E12</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> <b> such that </b><br/><a NAME="E6:12"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="substut2.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font></span><a href="substut2.html#K1" target="_self">]</a></span>
 <b>by </b><i><a class="txt" href="substut2.html#E4:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="substut2.html#T10" target="_self">Th10</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<b>thus </b><a NAME="E7:12"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K15">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <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="substut2.html#E6:12"><i><font color="Green">E14</font></i></a>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>


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