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<span class="kw">let </span><font color="Maroon" title="c1">alpha</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g</font> being   <a href="cgames_1.html#NM1" title="CGAMES_1:NM.1">ConwayGame</a> holds <br/> (  <a href="cgames_1.html#K9" title="CGAMES_1:func.9">ConwayRank</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> iff  ex <font color="Olive" title="b2">beta</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <br/>( <font color="Olive" title="b2">beta</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> &amp; <font color="Olive" title="b1">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Olive" title="b2">beta</font> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">g</font> be   <a href="cgames_1.html#NM1" title="CGAMES_1:NM.1">ConwayGame</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cgames_1.html#K9" title="CGAMES_1:func.9">ConwayRank</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> iff  ex <font color="Olive" title="b1">beta</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <br/>( <font color="Olive" title="b1">beta</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> &amp; <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Olive" title="b1">beta</font> ) )</span><br/>



<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">beta</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <br/>( <font color="Olive" title="b1">beta</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> &amp; <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Olive" title="b1">beta</font> ) implies  <a href="cgames_1.html#K9" title="CGAMES_1:func.9">ConwayRank</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:31_1"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
 <a href="cgames_1.html#K9" title="CGAMES_1:func.9">ConwayRank</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">beta</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <br/>( <font color="Olive" title="b1">beta</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> &amp; <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Olive" title="b1">beta</font> )</span><br/><span class="kw">take </span><font color="Maroon" title="c3">beta</font> =  <a href="cgames_1.html#K9" title="CGAMES_1:func.9">ConwayRank</a> <font color="Maroon" title="c2">g</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">beta</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> &amp; <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Maroon" title="c3">beta</font> )</span><br/><span class="kw">thus </span><a NAME="E2:31_1"/>
<font color="Maroon" title="c3">beta</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31_1"><span class="lab"><font color="Green" title="E20">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Maroon" title="c3">beta</font></span><br/><span class="kw">thus </span><a NAME="E3:31_1"/>
<font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Maroon" title="c3">beta</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cgames_1.html#T12" target="_self" title="CGAMES_1:th.12">Th12</a></span>; <a class="txt" 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>

<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:31_2"/>
 ex <font color="Olive" title="b1">beta</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> st <br/>( <font color="Olive" title="b1">beta</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> &amp; <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Olive" title="b1">beta</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="cgames_1.html#K9" title="CGAMES_1:func.9">ConwayRank</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">beta</font> being   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a><span class="kw"> such that </span><br/><a NAME="E3:31_2"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
( <font color="Maroon" title="c3">beta</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font> &amp; <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cgames_1.html#K2" title="CGAMES_1:func.2">ConwayDay</a> <font color="Maroon" title="c3">beta</font> )
 ;<br/><a NAME="E4:31_2"/>
 <a href="cgames_1.html#K9" title="CGAMES_1:func.9">ConwayRank</a> <font color="Maroon" title="c2">g</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">beta</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cgames_1.html#T12" target="_self" title="CGAMES_1:th.12">Th12</a>, <a class="txt" href="#E3:31_2"><span class="lab"><font color="Green" title="E20">A2</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:31_2"/>
 <a href="cgames_1.html#K9" title="CGAMES_1:func.9">ConwayRank</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">alpha</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:31_2"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="ref" href="ordinal1.html#T12" title="ORDINAL1:th.12">ORDINAL1:12</a></span>; <a class="txt" 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>


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