<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="prelamb.html#R1" title="PRELAMB:pred.1">represents</a> <a onclick="hs(this)" href="javascript:()">PRELAMB:def 9 : <br/></a><span> for <font color="Olive" title="b1">s</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="prelamb.html#L1" title="PRELAMB:struct.1">typealg</a> <br/>  for <font color="Olive" title="b2">Tr</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="trees_2.html#NM5" title="TREES_2:NM.5">DecoratedTree</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">s</font><br/>  for <font color="Olive" title="b3">x</font> being   <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Olive" title="b1">s</font> holds <br/> ( <font color="Olive" title="b2">Tr</font> <a href="prelamb.html#R1" title="PRELAMB:pred.1">represents</a> <font color="Olive" title="b3">x</font> iff (  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">Tr</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  &amp; (  for <font color="Olive" title="b4">v</font> being    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">Tr</font> holds <br/> ( (  <a href="trees_2.html#K8" title="TREES_2:func.8">branchdeg</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or  <a href="trees_2.html#K8" title="TREES_2:func.8">branchdeg</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 ) &amp; (  <a href="trees_2.html#K8" title="TREES_2:func.8">branchdeg</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Olive" title="b2">Tr</font> <a href="prelamb.html#K4" title="PRELAMB:func.4">.</a> <font color="Olive" title="b4">v</font> is  <a href="prelamb.html#V6" title="PRELAMB:attr.6">primitive</a>  ) &amp; (  <a href="trees_2.html#K8" title="TREES_2:func.8">branchdeg</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 implies  ex <font color="Olive" title="b5">y</font>, <font color="Olive" title="b6">z</font> being   <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Olive" title="b1">s</font> st <br/>( ( <font color="Olive" title="b2">Tr</font> <a href="prelamb.html#K4" title="PRELAMB:func.4">.</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y</font> <a href="prelamb.html#K2" title="PRELAMB:func.2">/"</a> <font color="Olive" title="b6">z</font> or <font color="Olive" title="b2">Tr</font> <a href="prelamb.html#K4" title="PRELAMB:func.4">.</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Olive" title="b6">z</font> or <font color="Olive" title="b2">Tr</font> <a href="prelamb.html#K4" title="PRELAMB:func.4">.</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y</font> <a href="prelamb.html#K3" title="PRELAMB:func.3">*</a> <font color="Olive" title="b6">z</font> ) &amp; <font color="Olive" title="b2">Tr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y</font> &amp; <font color="Olive" title="b2">Tr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">v</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">z</font> ) ) ) ) ) );<br/></span></div>
