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<span class="kw">consider </span><font color="Maroon" title="c2">S1</font>, <font color="Maroon" title="c3">S2</font> being    <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> <span class="kw"> such that </span><br/><a NAME="E2:55_1_1"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
( <font color="Maroon" title="c1">S</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="c2">S1</font>,<font color="Maroon" title="c3">S2</font> &amp; <font color="Maroon" title="c2">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">S2</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="substut1.html#D27" target="_self" title="SUBSTUT1:def.27">Def27</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">S2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">S9</font> being   <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>  st <br/>( <font color="Maroon" title="c1">S</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="Olive" title="b1">S9</font>,<font color="Maroon" title="c3">S2</font> &amp; <font color="Olive" title="b1">S9</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">S2</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:55_1_1"/>
 ex <font color="Olive" title="b1">S9</font> being   <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>  st <br/>( <font color="Maroon" title="c1">S</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="Olive" title="b1">S9</font>,<font color="Maroon" title="c3">S2</font> &amp; <font color="Olive" title="b1">S9</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">S2</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55_1_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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