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<b>let </b><font color="Maroon">S1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> ;<br/><b>let </b><font color="Maroon">S2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="substut1.html#K38">CQC-Sub-WFF</a> ;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">S1</font> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">S2</font> <a href="substut1.html#K19">`2</a> 
 ;<br/>

<a NAME="E2:29"/><b>then </b>
 <a href="substut1.html#K21">Sub_&amp;</a> <font color="Maroon">S1</font>,<font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">S1</font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">S2</font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">S1</font> <a href="substut1.html#K19">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="ref" href="substut1.html#D21">SUBSTUT1:def 21</a></i>;<br/>
<a NAME="E3:29"/><b>then </b>
 <a href="sublemma.html#K7" target="_self">CQCSub_&amp;</a> <font color="Maroon">S1</font>,<font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">S1</font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon">S2</font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">S1</font> <a href="substut1.html#K19">`2</a> </span>)</span></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:29"/>
( <span class="p1">(<span class="default"><a href="sublemma.html#K7" target="_self">CQCSub_&amp;</a> <font color="Maroon">S1</font>,<font color="Maroon">S2</font></span>)</span> <a href="sublemma.html#K2" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">S1</font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span> <a href="cqc_lang.html#K11">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon">S2</font> <a href="sublemma.html#K2" target="_self">`1</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="sublemma.html#K7" target="_self">CQCSub_&amp;</a> <font color="Maroon">S1</font>,<font color="Maroon">S2</font></span>)</span> <a href="substut1.html#K19">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">S1</font> <a href="substut1.html#K19">`2</a>  )
 <b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>


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