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<b>let </b><font color="Maroon">F</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="relat_1.html#V2">non-empty</a>  <a href="finseq_1.html#M2">FinSequence</a> of  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">B</font> be    <a href="hallmar1.html#M3" target="_self">Singlification</a> of <font color="Maroon">A</font>,<font color="Maroon">i</font>;<br/><b>let </b><font color="Maroon">C</font> be    <a href="hallmar1.html#M3" target="_self">Singlification</a> of <font color="Maroon">B</font>,<font color="Maroon">j</font>;<br/>









<b>assume </b><a NAME="E1:36"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<a NAME="E2:36"/><i><font color="Green">E24</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="txt" href="hallmar1.html#E1:36"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E3:36"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="txt" href="hallmar1.html#E7:36"><i><font color="Green">E30</font></i></a>, </i>;<br/>
<a NAME="E4:36"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">C</font> is    <a href="hallmar1.html#M2" target="_self">Reduction</a> of <font color="Maroon">A</font>
 
<b>by </b><i><a class="txt" href="hallmar1.html#E5:36"><i><font color="Green">E28</font></i></a></i>;<br/>
<a NAME="E5:36"/><i><font color="Green">E28</font></i>: 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="hallmar1.html#E7:36"><i><font color="Green">E30</font></i></a>, , <a class="txt" href="hallmar1.html#E2:36"><i><font color="Green">E24</font></i></a></i>;<br/>
<a NAME="E6:36"/><i><font color="Green">E29</font></i>: 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="txt" href="hallmar1.html#E7:36"><i><font color="Green">E30</font></i></a>, , <a class="txt" href="hallmar1.html#E2:36"><i><font color="Green">E24</font></i></a></i>;<br/>
<a NAME="E7:36"/><i><font color="Green">E30</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="hallmar1.html#E7:36"><i><font color="Green">E30</font></i></a>, <a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/>
<a NAME="E8:36"/>
<font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 
<b>by </b><i><a class="txt" href="hallmar1.html#E7:36"><i><font color="Green">E30</font></i></a>, , <a class="txt" href="hallmar1.html#E1:36"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E9:36"/><b>then </b>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i>, <a class="ref" href="card_1.html#T80">CARD_1:80</a></i>;<br/>
<a NAME="E10:36"/><b>then </b>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="cqc_the1.html#T2">CQC_THE1:2</a></i>;<br/>
<b>hence </b><a NAME="E11:36"/>
( <font color="Maroon">C</font> is    <a href="hallmar1.html#M3" target="_self">Singlification</a> of <font color="Maroon">A</font>,<font color="Maroon">j</font> &amp; <font color="Maroon">C</font> is    <a href="hallmar1.html#M3" target="_self">Singlification</a> of <font color="Maroon">A</font>,<font color="Maroon">i</font> )
 <b>by </b><i><a class="txt" href="hallmar1.html#E7:36"><i><font color="Green">E30</font></i></a>, , , , <a class="txt" href="hallmar1.html#E2:36"><i><font color="Green">E24</font></i></a></i>;<br/>


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