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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E50">Def38</font></span>   defines <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> <a onclick="hs(this)" href="javascript:()">WAYBEL_0:def 38 : <br/></a><span> for <font color="Olive" title="b1">S</font>, <font color="Olive" title="b2">T</font> being    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b3">f</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> holds <br/> ( (  not <font color="Olive" title="b1">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Olive" title="b2">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  implies ( <font color="Olive" title="b3">f</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>  iff ( <font color="Olive" title="b3">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b3">f</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  &amp;  ex <font color="Olive" title="b4">g</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> st <br/>( <font color="Olive" title="b4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  &amp; <font color="Olive" title="b4">g</font> is  <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>  ) ) ) ) &amp; ( ( <font color="Olive" title="b1">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or <font color="Olive" title="b2">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) implies ( <font color="Olive" title="b3">f</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>  iff ( <font color="Olive" title="b1">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Olive" title="b2">T</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) ) ) );<br/></span></div>
