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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E24">Def9</font></span>   defines <a href="surreali.html#K7" title="SURREALI:func.7">||.</a> <a onclick="hs(this)" href="javascript:()">SURREALI:def 9 : <br/></a><span> for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> is   <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> holds <br/> for <font color="Olive">b<sub>2</sub></font> being   <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> iff  for <font color="Olive" title="b3">y</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> holds <br/> ( (  not <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive">b<sub>2</sub></font> or <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  or ( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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">y</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  ) ) &amp; ( ( <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreal0.html#K11" title="SURREAL0:func.11">0_No</a>  or ( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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">y</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  ) ) implies <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive">b<sub>2</sub></font> implies ( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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">y</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  ) ) &amp; ( <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</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">y</font> is  <a href="surreali.html#V2" title="SURREALI:attr.2">positive</a>  implies <font color="Olive" title="b3">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive">b<sub>2</sub></font> ) ) );<br/></span></div>
