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<b>let </b><font color="Maroon">S</font> be  <a href="osalg_4.html#V2" target="_self">locally_directed</a> <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">U1</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">S</font>, <font color="Maroon">U2</font> be  <a href="msualg_1.html#V5">non-empty</a> <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">F</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">U1</font>,<font color="Maroon">U2</font>;<br/>





<b>assume </b><a NAME="E1:58"/>
( <font color="Maroon">F</font> <a href="msualg_3.html#R2">is_epimorphism</a> <font color="Maroon">U1</font>,<font color="Maroon">U2</font> &amp; <font color="Maroon">F</font> is <a href="osalg_3.html#V1">order-sorted</a> )
 ;<br/>

<a NAME="E2:58"/><b>then </b>
 <a href="osalg_4.html#K21" target="_self">OSHomQuot</a> <font color="Maroon">F</font> <a href="msualg_3.html#R4">is_isomorphism</a>  <a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">U1</font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K19" target="_self">OSCng</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">U2</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:58"/>
 <a href="osalg_4.html#K16" target="_self">QuotOSAlg</a> <font color="Maroon">U1</font>,<span class="p1">(<span class="default"><a href="osalg_4.html#K19" target="_self">OSCng</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">U2</font> <a href="msualg_3.html#R6">are_isomorphic</a> 
 <b>by </b><i><a class="ref" href="msualg_3.html#D13">MSUALG_3:def 13</a></i>;<br/>


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