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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th6</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: SURREALI:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">o</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b3">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="Olive" title="b2">o</font>,<font color="Olive" title="b3">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="surreali.html#K3" title="SURREALI:func.3">divset</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Olive" title="b2">o</font>,<span class="p3">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b2">o</font></span>)</span>,<font color="Olive" title="b3">Inv</font>)</span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="surreali.html#K3" title="SURREALI:func.3">divset</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Olive" title="b2">o</font>,<span class="p2">(<span class="default"><a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive" title="b2">o</font></span>)</span>,<font color="Olive" title="b3">Inv</font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><a href="surreali.html#K3" title="SURREALI:func.3">divset</a> (<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Olive" title="b2">o</font>,<span class="p3">(<span class="default"><a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive" title="b2">o</font></span>)</span>,<font color="Olive" title="b3">Inv</font>)</span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="surreali.html#K3" title="SURREALI:func.3">divset</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">Inv</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Olive" title="b2">o</font>,<span class="p2">(<span class="default"><a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b2">o</font></span>)</span>,<font color="Olive" title="b3">Inv</font>)</span>)</span> )</div></div>
