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

<b>let </b><font color="Maroon">P</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">OAF</font> be    <a href="msalimit.html#M1" target="_self">OrderedAlgFam</a> of <font color="Maroon">P</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="msalimit.html#M2" target="_self">Binding</a> of <font color="Maroon">OAF</font>;<br/><b>let </b><font color="Maroon">i</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">P</font>;<br/><b>let </b><font color="Maroon">j</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">P</font>;<br/>











<b>assume </b><a NAME="E1:8"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">i</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j</font>
 ;<br/>

<b>let </b><font color="Maroon">f</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">j</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:8"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">f</font> <a href="pboole.html#R6">=</a>  <a href="msalimit.html#K1" target="_self">bind</a> <font color="Maroon">B</font>,<font color="Maroon">i</font>,<font color="Maroon">j</font>
 ;<br/>

<a NAME="E3:8"/>
<font color="Maroon">j</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T24">ORDERS_2:24</a></i>;<br/>
<b>then consider </b><font color="Maroon">f1</font> being   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">j</font></span>)</span>, <font color="Maroon">f2</font> being   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">j</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">j</font></span>)</span><b> such that </b><br/><a NAME="E5:8"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">j</font>,<font color="Maroon">i</font> &amp; <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">j</font>,<font color="Maroon">j</font> &amp; <font color="Maroon">B</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">j</font>,<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">f1</font> &amp; <font color="Maroon">f1</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">i</font>,<font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">j</font> )
 <b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E6:8"/>
<font color="Maroon">f</font> <a href="msualg_3.html#R1">is_homomorphism</a> <font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">i</font>,<font color="Maroon">OAF</font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, , , </i>;<br/>


</div>
