<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E32">Def11</font></span>   defines <a href="surreali.html#K9" title="SURREALI:func.9">No_inverse_op</a> <a onclick="hs(this)" href="javascript:()">SURREALI:def 11 : <br/></a><span> for <font color="Olive" title="b1">A</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a><br/>  for <font color="Olive">b<sub>2</sub></font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="surreali.html#K8" title="SURREALI:func.8">Positives</a> <font color="Olive" title="b1">A</font> holds <br/> ( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="surreali.html#K9" title="SURREALI:func.9">No_inverse_op</a> <font color="Olive" title="b1">A</font> iff  ex <font color="Olive" title="b3">S</font> being   <a href="cohsp_1.html#V6" title="COHSP_1:attr.6">c=-monotone</a>   <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a>  <a href="ordinal1.html#NM4" title="ORDINAL1:NM.4">Sequence</a> st <br/>(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Olive" title="b1">A</font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">A</font> &amp; (  for <font color="Olive" title="b4">B</font> being   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>  st <font color="Olive" title="b4">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <font color="Olive" title="b1">A</font> holds <br/> ex <font color="Olive" title="b5">SB</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="surreali.html#K8" title="SURREALI:func.8">Positives</a> <font color="Olive" title="b4">B</font> st <br/>( <font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">SB</font> &amp; (  for <font color="Olive" title="b6">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="surreali.html#K8" title="SURREALI:func.8">Positives</a> <font color="Olive" title="b4">B</font> holds <br/><font color="Olive" title="b5">SB</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p3">(<span class="default"><a href="surreali.html#K5" title="SURREALI:func.5">divL</a> (<span class="p4"><a href="surreali.html#K7" title="SURREALI:func.7">||.</a><span class="default"><font color="Olive" title="b6">x</font></span><a href="surreali.html#K7" title="SURREALI:func.7">.||</a></span>,<span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p0">(<span class="default"><font color="Olive" title="b3">S</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b4">B</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <span class="p3">(<span class="default"><a href="surreali.html#K6" title="SURREALI:func.6">divR</a> (<span class="p4"><a href="surreali.html#K7" title="SURREALI:func.7">||.</a><span class="default"><font color="Olive" title="b6">x</font></span><a href="surreali.html#K7" title="SURREALI:func.7">.||</a></span>,<span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5">(<span class="default"><a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p0">(<span class="default"><font color="Olive" title="b3">S</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a> <font color="Olive" title="b4">B</font></span>)</span></span>)</span></span>)</span>)</span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> ) ) ) ) );<br/></span></div>
