<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: ORDERS_5:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font> holds <br/> ( ( <font color="Olive" title="b2">a1</font> <a href="orders_5.html#R3" title="ORDERS_5:pred.3">&lt;~</a> <font color="Olive" title="b3">a2</font> &amp; <font color="Olive" title="b3">a2</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b4">a3</font> implies <font color="Olive" title="b2">a1</font> <a href="orders_5.html#R3" title="ORDERS_5:pred.3">&lt;~</a> <font color="Olive" title="b4">a3</font> ) &amp; ( <font color="Olive" title="b2">a1</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b3">a2</font> &amp; <font color="Olive" title="b3">a2</font> <a href="orders_5.html#R3" title="ORDERS_5:pred.3">&lt;~</a> <font color="Olive" title="b4">a3</font> implies <font color="Olive" title="b2">a1</font> <a href="orders_5.html#R3" title="ORDERS_5:pred.3">&lt;~</a> <font color="Olive" title="b4">a3</font> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_2.html#T3" onmouseover="rs('orders_2/T3')" onmouseout="rh()">ORDERS_2:3</a></span>;<br/></div></div>
