<?xml version="1.0"?>
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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b3">v</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">B</font> holds <br/>( <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Olive" title="b1">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">B</font>,<font color="Maroon" title="c2">k</font>) iff  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b2">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>  st <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">B</font> holds <br/>( <font color="Olive" title="b1">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">k</font>) iff  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">v</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">B</font> implies ( <font color="Maroon" title="c5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">k</font>) iff  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:11"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">B</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">k</font>) iff  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> )</span><br/>

<a NAME="E2:11"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Maroon" title="c5">v</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
;<br/>
<a NAME="E3:11"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/>
<a NAME="E4:11"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ballot_1.html#T6" target="_self" onmouseover="rs('ballot_1/T6')" onmouseout="rh()">Th6</a>, <a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E11">A1</font></span></a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:11"/>
( <font color="Maroon" title="c5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">k</font>) implies  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font> implies <font color="Maroon" title="c5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">k</font>) )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="11_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:11_1"/>
<font color="Maroon" title="c5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">k</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font></span><br/>

<a NAME="E2:11_1"/><span class="kw">then </span>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">A</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ballot_1.html#D1" target="_self" onmouseover="rs('ballot_1/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:11_1"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E13">A3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E6:11"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c4">B</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">k</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">k</font>)</span><br/>

<span class="kw">hence </span><a NAME="E7:11"/>
<font color="Maroon" title="c5">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K1" title="BALLOT_1:func.1">Election</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">k</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="ballot_1.html#D1" target="_self" onmouseover="rs('ballot_1/D1')" onmouseout="rh()">Def1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
