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<div><span class="kw">theorem </span><a NAME="T44"><span class="comment"><font color="firebrick">:: YELLOW_7:44</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being   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><br/>  for <font color="Olive" title="b3">f1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">T</font><br/>  for <font color="Olive" title="b4">g1</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">T</font>,<font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b5">f2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">T</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a></span>)</span><br/>  for <font color="Olive" title="b6">g2</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">T</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a></span>)</span>  st <font color="Olive" title="b3">f1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">f2</font> &amp; <font color="Olive" title="b4">g1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b6">g2</font> holds <br/>( <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Olive" title="b3">f1</font>,<font color="Olive" title="b4">g1</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  iff <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Olive" title="b6">g2</font>,<font color="Olive" title="b5">f2</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>  )</div></div>
