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<a NAME="E1:139_1_1"/><span class="lab"><font color="Green" title="E106">A1</font></span>: 
<font color="Maroon" title="c1">alpha</font> <a href="surrealr.html#K8" title="SURREALR:func.8">+</a> <font color="Maroon" title="c2">beta</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Maroon" title="c1">alpha</font></span>)</span> <a href="surrealr.html#K9" title="SURREALR:func.9">++</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">beta</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">alpha</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="surrealr.html#K9" title="SURREALR:func.9">++</a> <span class="p4">(<span class="default"><a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Maroon" title="c2">beta</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Maroon" title="c1">alpha</font></span>)</span> <a href="surrealr.html#K9" title="SURREALR:func.9">++</a> <span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">beta</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">alpha</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="surrealr.html#K9" title="SURREALR:func.9">++</a> <span class="p4">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Maroon" title="c2">beta</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealr.html#T28" onmouseover="rs('surrealr/T28')" onmouseout="rh()">SURREALR:28</a></span>;<br/>
<a NAME="E2:139_1_1"/>
(  <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Maroon" title="c1">alpha</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Maroon" title="c2">beta</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealn.html#D10" target="_self" onmouseover="rs('surrealn/D10')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E3:139_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Maroon" title="c1">alpha</font></span>)</span> <a href="surrealr.html#K9" title="SURREALR:func.9">++</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">beta</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">alpha</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="surrealr.html#K9" title="SURREALR:func.9">++</a> <span class="p1">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Maroon" title="c2">beta</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surrealr.html#T27" onmouseover="rs('surrealr/T27')" onmouseout="rh()">SURREALR:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:139_1_1"/>
<font color="Maroon" title="c1">alpha</font> <a href="surrealr.html#K8" title="SURREALR:func.8">+</a> <font color="Maroon" title="c2">beta</font> is  <a href="surrealn.html#V3" title="SURREALN:attr.3">No_ordinal</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:139_1_1"><span class="lab"><font color="Green" title="E106">A1</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/>


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