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<div><span class="kw">theorem </span><a NAME="T24"><span class="comment"><font color="firebrick">:: OSALG_4:24</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">U2</font> being   <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>   <a href="osalg_1.html#V13" title="OSALG_1:attr.13">monotone</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="b4">F</font> being   <a href="msualg_3.html#NM1" title="MSUALG_3:NM.1">ManySortedFunction</a> of <font color="Olive" title="b2">U1</font>,<font color="Olive" title="b3">U2</font>  st <font color="Olive" title="b4">F</font> <a href="msualg_3.html#R1" title="MSUALG_3:pred.1">is_homomorphism</a> <font color="Olive" title="b2">U1</font>,<font color="Olive" title="b3">U2</font> &amp; <font color="Olive" title="b4">F</font> is  <a href="osalg_3.html#V1" title="OSALG_3:attr.1">order-sorted</a>  holds <br/> <a href="osalg_4.html#K19" title="OSALG_4:func.19">OSCng</a> <font color="Olive" title="b4">F</font> is  <a href="osalg_4.html#V3" title="OSALG_4:attr.3">monotone</a> </div></div>
