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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font>,<font color="Maroon">Y</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>







<a NAME="E1:61"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> &amp;  <a href="supinf_2.html#K7" target="_self">rng</a> <font color="Maroon">F</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E2:61"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">F</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="supinf_2.html#K7" target="_self">rng</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>thus </b><a NAME="E3:61"/>
(  <a href="supinf_2.html#K9" target="_self">inf</a> <font color="Maroon">F</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">F</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">F</font> <a href="supinf_2.html#K10" target="_self">.</a> <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_2.html#K8" target="_self">sup</a> <font color="Maroon">F</font> )
 <b>by </b><i>, <a class="ref" href="supinf_1.html#T76">SUPINF_1:76</a>, <a class="ref" href="supinf_1.html#T79">SUPINF_1:79</a></i>;<br/>


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