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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">f</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b3">f</font> is <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> <a href="ballot_1.html#V1" title="BALLOT_1:attr.1">-dominated-election</a>  holds <br/><font color="Olive" title="b3">f</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="Olive" title="b1">A</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">f</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">f</font> is <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 href="ballot_1.html#V1" title="BALLOT_1:attr.1">-dominated-election</a>  holds <br/><font color="Olive" title="b1">f</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="c3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">f</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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"> ( <font color="Maroon" title="c5">f</font> is <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 href="ballot_1.html#V1" title="BALLOT_1:attr.1">-dominated-election</a>  implies <font color="Maroon" title="c5">f</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="c3">A</font> )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">f1</font> = <font color="Maroon" title="c5">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1;<br/>
<span class="kw">assume </span><a NAME="E1:24"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c5">f</font> is <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 href="ballot_1.html#V1" title="BALLOT_1:attr.1">-dominated-election</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"> <font color="Maroon" title="c5">f</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="c3">A</font></span><br/>

<a NAME="E2:24"/><span class="kw">then </span>
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ballot_1.html#T15" target="_self" onmouseover="rs('ballot_1/T15')" onmouseout="rh()">Th14</a></span>;<br/>
<a NAME="E3:24"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E4:24"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T59" onmouseover="rs('finseq_1/T59')" onmouseout="rh()">FINSEQ_1:59</a></span>;<br/>
<a NAME="E5:24"/>
 <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">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1</span>)</span> <a href="relat_1.html#K8" title="RELAT_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="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</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">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1</span>)</span> <a href="relat_1.html#K8" title="RELAT_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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E21">A1</font></span></a></span>;<br/>
<a NAME="E6:24"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A3</font></span>: 
 not <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1</span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><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> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 
;<br/>
<a NAME="E7:24"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a>, <a class="txt" href="#E4:24"><span class="lab"><font color="Green" title="E22">A2</font></span></a></span>;<br/>
<a NAME="E8:24"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1</span>)</span> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p1"><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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T132" onmouseover="rs('relat_1/T132')" onmouseout="rh()">RELAT_1:132</a>, <a class="ref" href="finseq_1.html#T2" onmouseover="rs('finseq_1/T2')" onmouseout="rh()">FINSEQ_1:2</a>, <a class="txt" href="#E6:24"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#T33" onmouseover="rs('zfmisc_1/T33')" onmouseout="rh()">ZFMISC_1:33</a></span>;<br/>
<a NAME="E9:24"/>
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default">1</span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T2" onmouseover="rs('finseq_1/T2')" onmouseout="rh()">FINSEQ_1:2</a></span>;<br/>
<a NAME="E10:24"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><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 class="kw">by</span> <span class="lab"><a class="txt" href="#E8:24"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="funct_1.html#D7" onmouseover="rs('funct_1/D7')" onmouseout="rh()">FUNCT_1:def 7</a></span>;<br/>
<a NAME="E11:24"/><span class="kw">then </span>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> 1</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:24"/>
<font color="Maroon" title="c5">f</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="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T112" onmouseover="rs('finseq_3/T112')" onmouseout="rh()">FINSEQ_3:112</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/>


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