<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T13"><span class="comment"><font color="firebrick">:: OSALG_4:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="osalg_4.html#V2" title="OSALG_4:attr.2">locally_directed</a>  <a href="osalg_1.html#NM3" title="OSALG_1:NM.3">OrderSortedSign</a><br/>  for <font color="Olive" title="b2">U1</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  <a href="osalg_1.html#NM5" title="OSALG_1:NM.5">OSAlgebra</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">E</font> being   <a href="msualg_4.html#V2" title="MSUALG_4:attr.2">MSEquivalence-like</a>   <a href="osalg_4.html#M1" title="OSALG_4:mode.1">OrderSortedRelation</a> of <font color="Olive" title="b2">U1</font><br/>  for <font color="Olive" title="b4">s1</font>, <font color="Olive" title="b5">s2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b6">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">s1</font>  st <font color="Olive" title="b4">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b5">s2</font> holds <br/> for <font color="Olive" title="b7">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b2">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">s2</font>  st <font color="Olive" title="b7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">x</font> holds <br/> <a href="osalg_4.html#K8" title="OSALG_4:func.8">OSClass</a> (<font color="Olive" title="b3">E</font>,<font color="Olive" title="b6">x</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="osalg_4.html#K8" title="OSALG_4:func.8">OSClass</a> (<font color="Olive" title="b3">E</font>,<font color="Olive" title="b7">y</font>) <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_4.html#T4" target="_self" onmouseover="rs('osalg_4/T4')" onmouseout="rh()">Th4</a></span>;<br/></div></div>
