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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>thus </b> <a href="supinf_2.html#K9" target="_self">inf</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K12" target="_self">-</a> <font color="Maroon">F</font></span>)</span> = 
 <a href="supinf_1.html#K7">inf</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K6" target="_self">-</a> <span class="p2">(<span class="default"><a href="supinf_2.html#K7" target="_self">rng</a> <font color="Maroon">F</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T10" target="_self">Th10</a></i>
<br/>.= 
 <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K8" target="_self">sup</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T4" target="_self">Th4</a></i>
;<br/>

<b>thus </b> <a href="supinf_2.html#K8" target="_self">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K12" target="_self">-</a> <font color="Maroon">F</font></span>)</span> = 
 <a href="supinf_1.html#K6">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K6" target="_self">-</a> <span class="p2">(<span class="default"><a href="supinf_2.html#K7" target="_self">rng</a> <font color="Maroon">F</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T10" target="_self">Th10</a></i>
<br/>.= 
 <a href="supinf_2.html#K3" target="_self">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K9" target="_self">inf</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T5" target="_self">Th5</a></i>
;<br/>


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