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<span class="kw">let </span><font color="Maroon" title="c4">o</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="surreal0.html#D16" onmouseover="rs('surreal0/D16')" onmouseout="rh()">SURREAL0:def 16</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"> (  not <font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="surreali.html#K13" title="SURREALI:func.13">divset</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">Y</font>) or <font color="Maroon" title="c4">o</font> is  <a href="surreal0.html#V2" title="SURREAL0:attr.2">surreal</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:53_1_1"/>
<font color="Maroon" title="c4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="surreali.html#K13" title="SURREALI:func.13">divset</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">Y</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="c4">o</font> is  <a href="surreal0.html#V2" title="SURREAL0:attr.2">surreal</a> </span><br/>

<a NAME="E2:53_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">y1</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> st <br/>(  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  <a href="surrealo.html#NR3" title="SURREALO:NR.3">&lt;</a> <font color="Olive" title="b1">x1</font> &amp; <font color="Olive" title="b1">x1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">y1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c4">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a> <a href="surrealr.html#K8" title="SURREALR:func.8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">x1</font> <a href="surrealr.html#K10" title="SURREALR:func.10">-</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <font color="Olive" title="b2">y1</font></span>)</span></span>)</span> <a href="surrealr.html#K16" title="SURREALR:func.16">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x1</font> <a href="surreali.html#K12" title="SURREALI:func.12">"</a></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surreali.html#D15" target="_self" onmouseover="rs('surreali/D15')" onmouseout="rh()">Def15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:53_1_1"/>
<font color="Maroon" title="c4">o</font> is  <a href="surreal0.html#V2" title="SURREAL0:attr.2">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"> verum</span><br/>


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