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<span class="kw">let </span><font color="Maroon" title="c1">o</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">  for <font color="Olive" title="b1">Inv</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds <br/> ( <span class="p1">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Maroon" title="c1">o</font>,<font color="Olive" title="b1">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"><a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Maroon" title="c1">o</font>,<font color="Olive" title="b1">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">Inv</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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"> ( <span class="p1">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"><a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>



<a NAME="E1:8"/>
( <span class="p1">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="surreali.html#K4" title="SURREALI:func.4">transitions_of</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> &amp; <span class="p1">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="surreali.html#K4" title="SURREALI:func.4">transitions_of</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surreali.html#D5" target="_self" onmouseover="rs('surreali/D5')" onmouseout="rh()">Def5</a>, <a class="ref" href="surreali.html#D6" target="_self" onmouseover="rs('surreali/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<a NAME="E2:8"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a> &amp; <span class="p1">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <a href="surrealo.html#K1" title="SURREALO:func.1">1_No</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="surreali.html#D4" target="_self" onmouseover="rs('surreali/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:8"/>
( <span class="p1">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</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"><a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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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