<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">p</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">q</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">Sub</font> be   <a href="substut1.html#NM1">CQC_Substitution</a>;<br/>





<b>set </b><font color="Maroon">S1</font> = <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span>;<br/>
<b>set </b><font color="Maroon">S2</font> = <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span>;<br/>
<a NAME="E1:26"/><i><font color="Green">E43</font></i>: 
( <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="substut2.html#K5" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">Sub</font> &amp; <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="substut2.html#K5" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">Sub</font> &amp; <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="sublemma.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E2:26"/><b>then </b>
 <a href="sublemma.html#K7">CQCSub_&amp;</a> <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span>,<span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="substut1.html#K21">Sub_&amp;</a> <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span>,<span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span>
 
<b>by </b><i><a class="ref" href="sublemma.html#D4">SUBLEMMA:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:26"/>
<span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Maroon">q</font></span>)</span>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="sublemma.html#K7">CQCSub_&amp;</a> <span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span>,<span class="p1"><a href="substut2.html#K2" target="_self">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">Sub</font></span><a href="substut2.html#K2" target="_self">]</a></span>
 <b>by </b><i>, <a class="ref" href="substut1.html#D21">SUBSTUT1:def 21</a></i>;<br/>


</div>
