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<b>let </b><font color="Maroon" title="c1">F</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">F</font>;<br/><b>let </b><font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c5">B</font> be    <a href="hallmar1.html#M3" title="HALLMAR1:mode.3">Singlification</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">i</font>;<br/><b>let </b><font color="Maroon" title="c6">C</font> be    <a href="hallmar1.html#M3" title="HALLMAR1:mode.3">Singlification</a> of <font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c4">j</font>;<br/>









<b>assume </b><a NAME="E1:36"/><i><font color="Green" title="E30">A1</font></i>: 
( <font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c4">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/>

<a NAME="E2:36"/><i><font color="Green" title="E31">A2</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="hallmar1.html#D6" target="_self" title="HALLMAR1:def.6">Def6</a></i>;<br/>
<a NAME="E3:36"/><i><font color="Green" title="E32">A3</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="txt" href="hallmar1.html#E1:36"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="hallmar1.html#T2" target="_self" title="HALLMAR1:th.2">Th2</a></i>;<br/>
<a NAME="E4:36"/><i><font color="Green" title="E33">A4</font></i>: 
<font color="Maroon" title="c6">C</font> is    <a href="hallmar1.html#M2" title="HALLMAR1:mode.2">Reduction</a> of <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="hallmar1.html#T22" target="_self" title="HALLMAR1:th.22">Th22</a></i>;<br/>
<a NAME="E5:36"/><i><font color="Green" title="E34">A5</font></i>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="hallmar1.html#E1:36"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="hallmar1.html#E2:36"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="hallmar1.html#D7" target="_self" title="HALLMAR1:def.7">Def7</a></i>;<br/>
<a NAME="E6:36"/><i><font color="Green" title="E35">A6</font></i>: 
 <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="hallmar1.html#E1:36"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="hallmar1.html#E3:36"><i><font color="Green" title="E32">A3</font></i></a>, <a class="ref" href="hallmar1.html#D7" target="_self" title="HALLMAR1:def.7">Def7</a></i>;<br/>
<a NAME="E7:36"/><i><font color="Green" title="E36">A7</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="hallmar1.html#E1:36"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/>
<a NAME="E8:36"/>
<font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>
 
<b>by </b><i><a class="txt" href="hallmar1.html#E1:36"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="hallmar1.html#E2:36"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="hallmar1.html#D6" target="_self" title="HALLMAR1:def.6">Def6</a></i>;<br/>
<a NAME="E9:36"/><b>then </b>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="txt" href="hallmar1.html#E6:36"><i><font color="Green" title="E35">A6</font></i></a>, <a class="txt" href="hallmar1.html#E7:36"><i><font color="Green" title="E36">A7</font></i></a>, <a class="ref" href="nat_1.html#T26" title="NAT_1:th.26">NAT_1:26</a>, <a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</a></i>;<br/>
<b>hence </b><a NAME="E10:36"/>
( <font color="Maroon" title="c6">C</font> is    <a href="hallmar1.html#M3" title="HALLMAR1:mode.3">Singlification</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">j</font> &amp; <font color="Maroon" title="c6">C</font> is    <a href="hallmar1.html#M3" title="HALLMAR1:mode.3">Singlification</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">i</font> )
 <b>by </b><i><a class="txt" href="hallmar1.html#E1:36"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="hallmar1.html#E3:36"><i><font color="Green" title="E32">A3</font></i></a>, <a class="txt" href="hallmar1.html#E4:36"><i><font color="Green" title="E33">A4</font></i></a>, <a class="txt" href="hallmar1.html#E5:36"><i><font color="Green" title="E34">A5</font></i></a>, <a class="ref" href="hallmar1.html#D7" target="_self" title="HALLMAR1:def.7">Def7</a></i>;<br/>


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