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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">S1'</font>, <font color="Maroon" title="c4">S2'</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="substut1.html#K16" title="SUBSTUT1:func.16">QC-Sub-WFF</a> ;<br/>







<b>assume </b><a NAME="E1:62"/><i><font color="Green" title="E35">A1</font></i>: 
( <font color="Maroon" title="c1">S1</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="c2">S2</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  &amp; <font color="Maroon" title="c3">S1'</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="c4">S2'</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  &amp;  <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c3">S1'</font>,<font color="Maroon" title="c4">S2'</font> )
 ;<br/>

<a NAME="E2:62"/><b>then </b>
 <a href="substut1.html#K21" title="SUBSTUT1:func.21">Sub_&amp;</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font> <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"><span class="p3">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S2</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">S1</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>
 
<b>by </b><i><a class="ref" href="substut1.html#D21" target="_self" title="SUBSTUT1:def.21">Def21</a></i>;<br/>
<a NAME="E3:62"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">S2</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">S1</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="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">S1'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">S2'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">S1'</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>
 
<b>by </b><i><a class="txt" href="substut1.html#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="substut1.html#D21" target="_self" title="SUBSTUT1:def.21">Def21</a></i>;<br/>
<a NAME="E4:62"/><b>then </b><i><font color="Green" title="E36">A2</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S2</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">S1'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> <a href="qc_lang1.html#K13" title="QC_LANG1:func.13">'&amp;'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">S2'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span> &amp; <font color="Maroon" title="c1">S1</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="c3">S1'</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<a NAME="E5:62"/><i><font color="Green" title="E37">A3</font></i>: 
( <font color="Maroon" title="c1">S1</font> <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"><font color="Maroon" title="c1">S1</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">S1</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> &amp; <font color="Maroon" title="c3">S1'</font> <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"><font color="Maroon" title="c3">S1'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">S1'</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> )
 
<b>by </b><i><a class="ref" href="substut1.html#T10" target="_self" title="SUBSTUT1:th.10">Th10</a></i>;<br/>
<a NAME="E6:62"/>
( <font color="Maroon" title="c2">S2</font> <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"><font color="Maroon" title="c2">S2</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">S2</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> &amp; <font color="Maroon" title="c4">S2'</font> <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"><font color="Maroon" title="c4">S2'</font> <a href="substut1.html#K18" title="SUBSTUT1:func.18">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">S2'</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> )
 
<b>by </b><i><a class="ref" href="substut1.html#T10" target="_self" title="SUBSTUT1:th.10">Th10</a></i>;<br/>
<b>hence </b><a NAME="E7:62"/>
( <font color="Maroon" title="c1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S1'</font> &amp; <font color="Maroon" title="c2">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">S2'</font> )
 <b>by </b><i><a class="txt" href="substut1.html#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="substut1.html#E4:62"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="substut1.html#E5:62"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="qc_lang2.html#T3" title="QC_LANG2:th.3">QC_LANG2:3</a></i>;<br/>


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