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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th5</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: AOFA_I00:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font>, <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">v1</font>, <font color="Olive" title="b5">v2</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b5">v2</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b2">X</font>,<font color="Olive" title="b3">I</font>) holds <br/> for <font color="Olive" title="b6">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">X</font>,<font color="Olive" title="b1">N</font>  st <font color="Olive" title="b6">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b4">v1</font> <a href="aofa_i00.html#K17" title="AOFA_I00:func.17">**</a> (<font color="Olive" title="b6">f</font>,<font color="Olive" title="b1">N</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v2</font> <a href="aofa_i00.html#K17" title="AOFA_I00:func.17">**</a> (<font color="Olive" title="b6">f</font>,<font color="Olive" title="b1">N</font>) holds <br/><font color="Olive" title="b4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v2</font></div></div>
