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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: OSALG_4:15</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">R</font> being   <a href="osalg_4.html#NM4" title="OSALG_4:NM.4">OSCongruence</a> of <font color="Olive" title="b2">U1</font> holds <br/> (  <a href="osalg_4.html#K18" title="OSALG_4:func.18">OSNat_Hom</a> (<font color="Olive" title="b2">U1</font>,<font color="Olive" title="b3">R</font>) <a href="msualg_3.html#R2" title="MSUALG_3:pred.2">is_epimorphism</a> <font color="Olive" title="b2">U1</font>, <a href="osalg_4.html#K16" title="OSALG_4:func.16">QuotOSAlg</a> (<font color="Olive" title="b2">U1</font>,<font color="Olive" title="b3">R</font>) &amp;  <a href="osalg_4.html#K18" title="OSALG_4:func.18">OSNat_Hom</a> (<font color="Olive" title="b2">U1</font>,<font color="Olive" title="b3">R</font>) is  <a href="osalg_3.html#V1" title="OSALG_3:attr.1">order-sorted</a>  )</div></div>
