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<span class="kw">let </span><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">S19</font>, <font color="Maroon" title="c4">S29</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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">S19</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">S29</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">S19</font>,<font color="Maroon" title="c4">S29</font> implies ( <font color="Maroon" title="c1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S19</font> &amp; <font color="Maroon" title="c2">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">S29</font> ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:62"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E2:62"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c3">S19</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">S29</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a> 
 <span class="kw">and </span><br/><a NAME="E3:62"/><span class="lab"><font color="Green" title="E36">A3</font></span>: 
 <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">S19</font>,<font color="Maroon" title="c4">S29</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S19</font> &amp; <font color="Maroon" title="c2">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">S29</font> )</span><br/>

<a NAME="E4:62"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="substut1.html#D21" target="_self" title="SUBSTUT1:def.21">Def21</a></span>;<br/>
<a NAME="E5:62"/><span class="kw">then </span>
<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">S19</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">S29</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">S19</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="substut1.html#D21" target="_self" title="SUBSTUT1:def.21">Def21</a></span>;<br/>
<a NAME="E6:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A4</font></span>: 
( <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">S19</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">S29</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">S19</font> <a href="substut1.html#K19" title="SUBSTUT1:func.19">`2</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>;<br/>
<a NAME="E7:62"/><span class="lab"><font color="Green" title="E38">A5</font></span>: 
( <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">S29</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">S29</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">S29</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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T10" target="_self" title="SUBSTUT1:th.10">Th10</a></span>;<br/>
<a NAME="E8:62"/>
( <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">S19</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">S19</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">S19</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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="substut1.html#T10" target="_self" title="SUBSTUT1:th.10">Th10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:62"/>
( <font color="Maroon" title="c1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">S19</font> &amp; <font color="Maroon" title="c2">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">S29</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="txt" href="#E6:62"><span class="lab"><font color="Green" title="E37">A4</font></span></a>, <a class="txt" href="#E7:62"><span class="lab"><font color="Green" title="E38">A5</font></span></a>, <a class="ref" href="qc_lang2.html#T3" title="QC_LANG2:th.3">QC_LANG2:3</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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