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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</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">f1</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">f2</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/>









<b>assume </b><a NAME="E1:86"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">f1</font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> &amp; <font color="Maroon">f2</font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">Y</font> )
 ;<br/>

<a NAME="E2:86"/><b>then </b>
 <a href="comseq_1.html#K5">-</a> <font color="Maroon">f2</font> <a href="partfun2.html#R1">is_constant_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E3:86"/><b>then </b>
<font color="Maroon">f1</font> <a href="comseq_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="comseq_1.html#K5">-</a> <font color="Maroon">f2</font></span>)</span> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T24" target="_self">Th24</a>, <a class="ref" href="cfunct_1.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E4:86"/>
<font color="Maroon">f1</font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">f2</font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="comseq_1.html#D10">COMSEQ_1:def 10</a></i>;<br/>

<a NAME="E5:86"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">f2</font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">Y</font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T24" target="_self">Th24</a>, <a class="ref" href="cfunct_1.html#T21" target="_self">Th21</a></i>;<br/>
<b>hence </b><a NAME="E6:86"/>
<font color="Maroon">f2</font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">f1</font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T24" target="_self">Th24</a>, <a class="ref" href="cfunct_1.html#T18" target="_self">Th18</a></i>;<br/>

<b>thus </b><a NAME="E7:86"/>
<font color="Maroon">f1</font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">f2</font> <a href="cfunct_1.html#R1" target="_self">is_bounded_on</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T24" target="_self">Th24</a>, <a class="ref" href="cfunct_1.html#T26" target="_self">Th26</a>, <a class="ref" href="cfunct_1.html#T18" target="_self">Th18</a></i>;<br/>


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