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<div>:: <span class="kw">deftheorem </span>   defines <a href="field_8.html#V6" title="FIELD_8:attr.6">-isomorphism</a> <a onclick="hs(this)" href="javascript:()">FIELD_8:def 8 : <br/></a><span> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">S1</font>, <font color="Olive" title="b3">S2</font> being   <a href="field_4.html#NM1" title="FIELD_4:NM.1">RingExtension</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b4">h</font> being   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">S1</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">S2</font> holds <br/> ( <font color="Olive" title="b4">h</font> is <font color="Olive" title="b1">R</font> <a href="field_8.html#V6" title="FIELD_8:attr.6">-isomorphism</a>  iff  ex <font color="Olive" title="b5">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">S1</font>,<font color="Olive" title="b3">S2</font> st <br/>( <font color="Olive" title="b5">g</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">h</font> &amp; <font color="Olive" title="b5">g</font> is <font color="Olive" title="b1">R</font> <a href="field_8.html#V4" title="FIELD_8:attr.4">-isomorphism</a>  ) );<br/></span></div>
