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<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</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">x</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surreal0.html#K10" title="SURREAL0:func.10">Day</a> <font color="Maroon" title="c1">A</font> holds <br/><font color="Olive" title="b1">x</font> <a href="surrealo.html#R1" title="SURREALO:pred.1">&lt;=</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</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="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surreal0.html#K10" title="SURREAL0:func.10">Day</a> <font color="Maroon" title="c1">A</font> implies <font color="Maroon" title="c2">x</font> <a href="surrealo.html#R1" title="SURREALO:pred.1">&lt;=</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:134"/>
<font color="Maroon" title="c2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surreal0.html#K10" title="SURREAL0:func.10">Day</a> <font color="Maroon" title="c1">A</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="c2">x</font> <a href="surrealo.html#R1" title="SURREALO:pred.1">&lt;=</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font></span><br/>

<a NAME="E2:134"/><span class="kw">then </span>
( <font color="Maroon" title="c2">x</font> <a href="surrealo.html#R1" title="SURREALO:pred.1">&lt;=</a>  <a href="surrealn.html#K8" title="SURREALN:func.8">No_Ordinal_op</a> <font color="Maroon" title="c1">A</font> &amp;  <a href="surrealn.html#K8" title="SURREALN:func.8">No_Ordinal_op</a> <font color="Maroon" title="c1">A</font> <a href="surrealo.html#R2" title="SURREALO:pred.2">==</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#T69" target="_self" onmouseover="rs('surrealn/T69')" onmouseout="rh()">Th69</a>, <a class="ref" href="surrealn.html#T73" target="_self" onmouseover="rs('surrealn/T73')" onmouseout="rh()">Th73</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:134"/>
<font color="Maroon" title="c2">x</font> <a href="surrealo.html#R1" title="SURREALO:pred.1">&lt;=</a>  <a href="surrealn.html#K9" title="SURREALN:func.9">No_uOrdinal_op</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="surrealo.html#T4" onmouseover="rs('surrealo/T4')" onmouseout="rh()">SURREALO:4</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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