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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">Y</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K7" title="NUMBERS:func.7">ExtREAL</a> ;<br/><b>let </b><font color="Maroon" title="c3">F</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font>;<br/>





<b>thus </b> <a href="supinf_2.html#K11" title="SUPINF_2:func.11">inf</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K14" title="SUPINF_2:func.14">-</a> <font color="Maroon" title="c3">F</font></span>)</span> = 
 <a href="supinf_2.html#K7" title="SUPINF_2:func.7">inf</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K6" title="SUPINF_2:func.6">-</a> <span class="p2">(<span class="default"><a href="supinf_2.html#K9" title="SUPINF_2:func.9">rng</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T37" target="_self" title="SUPINF_2:th.37">Th37</a></i>
<br/>.= 
 <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K10" title="SUPINF_2:func.10">sup</a> <font color="Maroon" title="c3">F</font></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T32" target="_self" title="SUPINF_2:th.32">Th32</a></i>
;<br/>

<b>thus </b> <a href="supinf_2.html#K10" title="SUPINF_2:func.10">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K14" title="SUPINF_2:func.14">-</a> <font color="Maroon" title="c3">F</font></span>)</span> = 
 <a href="supinf_2.html#K8" title="SUPINF_2:func.8">sup</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K6" title="SUPINF_2:func.6">-</a> <span class="p2">(<span class="default"><a href="supinf_2.html#K9" title="SUPINF_2:func.9">rng</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T37" target="_self" title="SUPINF_2:th.37">Th37</a></i>
<br/>.= 
 <a href="supinf_2.html#K3" title="SUPINF_2:func.3">-</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K11" title="SUPINF_2:func.11">inf</a> <font color="Maroon" title="c3">F</font></span>)</span>
<b>by </b><i><a class="ref" href="supinf_2.html#T33" target="_self" title="SUPINF_2:th.33">Th33</a></i>
;<br/>


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