<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">R</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">z</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">R</font>,<font color="Olive" title="b1">z</font> is  <a href="osalg_1.html#V11" title="OSALG_1:attr.11">order-sorted</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">z</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">z</font> is  <a href="osalg_1.html#V11" title="OSALG_1:attr.11">order-sorted</a> </span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">x</font> =  <a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">z</font>;<br/>
<a NAME="E1:52"/>
for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">s2</font> holds <br/><span class="p1">(<span class="default"><a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#T15" target="_self" title="OSALG_1:th.15">Th15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:52"/>
 <a href="osalg_1.html#K4" title="OSALG_1:func.4">ConstOSSet</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">z</font> is  <a href="osalg_1.html#V11" title="OSALG_1:attr.11">order-sorted</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="osalg_1.html#D18" target="_self" title="OSALG_1:def.18">Def18</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
