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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>   st <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> &amp; <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/><span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Olive" title="b2">B</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K2" title="BALLOT_1:func.2">DominatedElection</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>)</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"> ( <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> &amp; <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 <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K2" title="BALLOT_1:func.2">DominatedElection</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">assume </span><span class="kw">that </span><br/><a NAME="E1:21"/><span class="lab"><font color="Green" title="E18">A1</font></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">and </span><br/><a NAME="E2:21"/><span class="lab"><font color="Green" title="E19">A2</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K2" title="BALLOT_1:func.2">DominatedElection</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/>

<a NAME="E3:21"/>
<font color="Maroon" title="c2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E18">A1</font></span></a></span>;<br/>
<a NAME="E4:21"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Maroon" title="c4">B</font></span>)</span> is <font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c4">B</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">k</font> <a href="ballot_1.html#V1" title="BALLOT_1:attr.1">-dominated-election</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ballot_1.html#T17" target="_self" onmouseover="rs('ballot_1/T17')" onmouseout="rh()">Th16</a>, <a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="ballot_1.html#T16" target="_self" onmouseover="rs('ballot_1/T16')" onmouseout="rh()">Th15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:21"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ballot_1.html#K2" title="BALLOT_1:func.2">DominatedElection</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="ref" href="ballot_1.html#D3" target="_self" onmouseover="rs('ballot_1/D3')" onmouseout="rh()">Def3</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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