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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E44">Th34</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: SURREALI:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a><br/>  for <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">nX</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">Y</font> being   <a href="surreal0.html#V3" title="SURREAL0:attr.3">surreal-membered</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">x</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  &amp; ( ( <font color="Olive" title="b2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b3">nX</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <span class="p1"><a href="surreali.html#K7" title="SURREALI:func.7">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="surreali.html#K7" title="SURREALI:func.7">.||</a></span> ) or ( <font color="Olive" title="b2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b3">nX</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <span class="p1"><a href="surreali.html#K7" title="SURREALI:func.7">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="surreali.html#K7" title="SURREALI:func.7">.||</a></span> ) ) holds <br/> <a href="surreali.html#K13" title="SURREALI:func.13">divset</a> (<font color="Olive" title="b2">X</font>,<span class="p1"><a href="surreali.html#K7" title="SURREALI:func.7">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="surreali.html#K7" title="SURREALI:func.7">.||</a></span>,<font color="Olive" title="b4">Y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreali.html#K3" title="SURREALI:func.3">divset</a> (<font color="Olive" title="b4">Y</font>,<span class="p1"><a href="surreali.html#K7" title="SURREALI:func.7">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="surreali.html#K7" title="SURREALI:func.7">.||</a></span>,<font color="Olive" title="b3">nX</font>,<span class="p1">(<span class="default"><a href="surreali.html#K11" title="SURREALI:func.11">No_inverses_on</a> <span class="p2"><a href="surreali.html#K7" title="SURREALI:func.7">||.</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="surreali.html#K7" title="SURREALI:func.7">.||</a></span></span>)</span>)</div></div>
