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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E26">thiso</font></span>: <a NAME="T28"><span class="comment"><font color="firebrick">:: FIELD_5:28</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">Z</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">r</font> being    <a href="field_5.html#M1" title="FIELD_5:mode.1">Renaming</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">Z</font> holds <br/> ( <font color="Olive" title="b3">r</font> <a href="field_5.html#K7" title="FIELD_5:func.7">"</a>  is  <a href="vectsp_1.html#V13" title="VECTSP_1:attr.13">additive</a>  &amp; <font color="Olive" title="b3">r</font> <a href="field_5.html#K7" title="FIELD_5:func.7">"</a>  is  <a href="group_6.html#V1" title="GROUP_6:attr.1">multiplicative</a>  &amp; <font color="Olive" title="b3">r</font> <a href="field_5.html#K7" title="FIELD_5:func.7">"</a>  is  <a href="group_1.html#V6" title="GROUP_1:attr.6">unity-preserving</a>  &amp; <font color="Olive" title="b3">r</font> <a href="field_5.html#K7" title="FIELD_5:func.7">"</a>  is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b3">r</font> <a href="field_5.html#K7" title="FIELD_5:func.7">"</a>  is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  )</div></div>
