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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">X</font>, <font color="Maroon" title="c4">Y</font> be  <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="c5">Fy</font> be  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>









<b>assume </b><a NAME="E1:68"/><i><font color="Green" title="E51">A1</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c5">Fy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c4">Y</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c6">P</font> = 0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>;<br/>
<a NAME="E2:68"/>
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> )
 
<b>by </b><i><a class="txt" href="card_fin.html#E1:68"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a>, <a class="ref" href="funct_4.html#T67" title="FUNCT_4:th.67">FUNCT_4:67</a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="card_2.html#T76" title="CARD_2:th.76">CARD_2:76</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">P</font> = 0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <b>by </b><i><a class="ref" href="funct_2.html#T3" title="FUNCT_2:th.3">FUNCT_2:3</a></i>;<br/>
<a NAME="E4:68"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T67" title="FUNCT_4:th.67">FUNCT_4:67</a></i>;<br/>
<a NAME="E5:68"/><b>then </b>
( <font color="Maroon" title="c7">P</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a>, <a class="ref" href="card_1.html#T66" title="CARD_1:th.66">CARD_1:66</a></i>;<br/>
<a NAME="E6:68"/><b>then </b>
( <font color="Maroon" title="c7">P</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">Fy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="txt" href="card_fin.html#E1:68"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="stirl2_1.html#T70" title="STIRL2_1:th.70">STIRL2_1:70</a>, <a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">XFS</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E8:68"/><i><font color="Green" title="E52">A2</font></i>: 
 <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c8">XFS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>and </b><br/><a NAME="E9:68"/><i><font color="Green" title="E53">A3</font></i>: 
for <font color="Olive" title="b1">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c8">XFS</font> holds <br/><font color="Maroon" title="c8">XFS</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">z</font></span>)</span>
 <b>and </b><br/><a NAME="E10:68"/><i><font color="Green" title="E54">A4</font></i>: 
 <a href="card_fin.html#K5" title="CARD_FIN:func.5">Card_Intersection</a> <font color="Maroon" title="c5">Fy</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="stirl2_1.html#K7" title="STIRL2_1:func.7">Sum</a> <font color="Maroon" title="c8">XFS</font>
 <b>by </b><i><a class="ref" href="card_fin.html#T52" target="_self" title="CARD_FIN:th.52">Th52</a></i>;<br/>
<a NAME="E11:68"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c7">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/>
<a NAME="E12:68"/><b>then </b>
(  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c8">XFS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default">0,1</span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c7">P</font> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c7">P</font> )
 
<b>by </b><i><a class="txt" href="card_fin.html#E1:68"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="card_fin.html#E8:68"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="card_2.html#T76" title="CARD_2:th.76">CARD_2:76</a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E13:68"/><b>then </b>
(  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c8">XFS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c8">XFS</font> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K2" title="AFINSQ_1:func.2">dom</a> <font color="Maroon" title="c8">XFS</font> &amp; <font color="Maroon" title="c7">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Maroon" title="c7">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> &amp; <font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span> )
 
<b>by </b><i><a class="txt" href="card_fin.html#E1:68"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="afinsq_1.html#D1" title="AFINSQ_1:def.1">AFINSQ_1:def 1</a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a>, <a class="ref" href="funct_1.html#T23" title="FUNCT_1:th.23">FUNCT_1:23</a></i>;<br/>
<a NAME="E14:68"/><b>then </b>
( <font color="Maroon" title="c8">XFS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="stirl2_1.html#K5" title="STIRL2_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">XFS</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> 0</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c8">XFS</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> 1</span>)</span></span><a href="stirl2_1.html#K5" title="STIRL2_1:func.5">%&gt;</a></span> &amp; <font color="Maroon" title="c8">XFS</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c8">XFS</font> <a href="stirl2_1.html#K8" title="STIRL2_1:func.8">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">Y</font> )
 
<b>by </b><i><a class="txt" href="card_fin.html#E9:68"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="afinsq_1.html#T42" title="AFINSQ_1:th.42">AFINSQ_1:42</a></i>;<br/>
<a NAME="E15:68"/><b>then </b>
<a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="stirl2_1.html#K4" title="STIRL2_1:func.4">"**"</a> <font color="Maroon" title="c8">XFS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="stirl2_1.html#T48" title="STIRL2_1:th.48">STIRL2_1:48</a></i>;<br/>
<a NAME="E16:68"/><b>then </b><i><font color="Green" title="E55">A5</font></i>: 
<a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="stirl2_1.html#K4" title="STIRL2_1:func.4">"**"</a> <font color="Maroon" title="c8">XFS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">Y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="binop_2.html#D23" title="BINOP_2:def.23">BINOP_2:def 23</a></i>;<br/>
<a NAME="E17:68"/>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E18:68"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="finsop_1.html#K3" title="FINSOP_1:func.3">--&gt;</a> 0</span>)</span> <a href="relset_1.html#K11" title="RELSET_1:func.11">"</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">0</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c5">Fy</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X</font> &amp; <font color="Maroon" title="c5">Fy</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">Y</font> )
 
<b>by </b><i><a class="txt" href="card_fin.html#E1:68"><i><font color="Green" title="E51">A1</font></i></a>, <a class="ref" href="card_2.html#T76" title="CARD_2:th.76">CARD_2:76</a>, <a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a>, <a class="ref" href="funcop_1.html#T20" title="FUNCOP_1:th.20">FUNCOP_1:20</a></i>;<br/>
<a NAME="E19:68"/><b>then </b>
(  <a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c5">Fy</font>,<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="finsop_1.html#K3" title="FINSOP_1:func.3">--&gt;</a> 0</span>)</span>,0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c4">Y</font> &amp;  <a href="card_fin.html#K5" title="CARD_FIN:func.5">Card_Intersection</a> <font color="Maroon" title="c5">Fy</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><a href="card_fin.html#K2" title="CARD_FIN:func.2">Intersection</a> <font color="Maroon" title="c5">Fy</font>,<span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="finsop_1.html#K3" title="FINSOP_1:func.3">--&gt;</a> 0</span>)</span>,0</span>)</span> )
 
<b>by </b><i><a class="ref" href="card_fin.html#T38" target="_self" title="CARD_FIN:th.38">Th38</a>, <a class="ref" href="card_fin.html#T53" target="_self" title="CARD_FIN:th.53">Th53</a></i>;<br/>
<b>hence </b><a NAME="E20:68"/>
(  <a href="card_fin.html#K5" title="CARD_FIN:func.5">Card_Intersection</a> <font color="Maroon" title="c5">Fy</font>,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c4">Y</font></span>)</span> &amp;  <a href="card_fin.html#K5" title="CARD_FIN:func.5">Card_Intersection</a> <font color="Maroon" title="c5">Fy</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c4">Y</font></span>)</span> )
 <b>by </b><i><a class="txt" href="card_fin.html#E16:68"><i><font color="Green" title="E55">A5</font></i></a>, <a class="txt" href="card_fin.html#E10:68"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="stirl2_1.html#D4" title="STIRL2_1:def.4">STIRL2_1:def 4</a></i>;<br/>


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