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<b>let </b><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">C</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="c4">f1</font>, <font color="Maroon" title="c5">f2</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c3">C</font>, <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>









<b>assume </b><a NAME="E1:86"/><i><font color="Green" title="E58">A1</font></i>: 
( <font color="Maroon" title="c4">f1</font> <a href="cfunct_1.html#R1" title="CFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Maroon" title="c5">f2</font> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c2">Y</font> )
 ;<br/>

<a NAME="E2:86"/><b>then </b>
 <a href="comseq_1.html#K5" title="COMSEQ_1:func.5">-</a> <font color="Maroon" title="c5">f2</font> <a href="partfun2.html#R1" title="PARTFUN2:pred.1">is_constant_on</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T92" target="_self" title="CFUNCT_1:th.92">Th92</a></i>;<br/>
<a NAME="E3:86"/><b>then </b>
<font color="Maroon" title="c4">f1</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <span class="p1">(<span class="default"><a href="comseq_1.html#K5" title="COMSEQ_1:func.5">-</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="cfunct_1.html#R1" title="CFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:86"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="cfunct_1.html#T95" target="_self" title="CFUNCT_1:th.95">Th95</a></i>;<br/>
<b>hence </b><a NAME="E4:86"/>
<font color="Maroon" title="c4">f1</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c5">f2</font> <a href="cfunct_1.html#R1" title="CFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="ref" href="comseq_1.html#D10" title="COMSEQ_1:def.10">COMSEQ_1:def 10</a></i>;<br/>

<a NAME="E5:86"/><i><font color="Green" title="E59">A2</font></i>: 
<font color="Maroon" title="c5">f2</font> <a href="cfunct_1.html#R1" title="CFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c2">Y</font>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:86"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="cfunct_1.html#T93" target="_self" title="CFUNCT_1:th.93">Th93</a></i>;<br/>
<b>hence </b><a NAME="E6:86"/>
<font color="Maroon" title="c5">f2</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c4">f1</font> <a href="cfunct_1.html#R1" title="CFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="txt" href="cfunct_1.html#E1:86"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="cfunct_1.html#T88" target="_self" title="CFUNCT_1:th.88">Th88</a></i>;<br/>

<b>thus </b><a NAME="E7:86"/>
<font color="Maroon" title="c4">f1</font> <a href="comseq_1.html#K3" title="COMSEQ_1:func.3">(#)</a> <font color="Maroon" title="c5">f2</font> <a href="cfunct_1.html#R1" title="CFUNCT_1:pred.1">is_bounded_on</a> <font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y</font>
 <b>by </b><i><a class="txt" href="cfunct_1.html#E1:86"><i><font color="Green" title="E58">A1</font></i></a>, <a class="txt" href="cfunct_1.html#E5:86"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="cfunct_1.html#T88" target="_self" title="CFUNCT_1:th.88">Th88</a></i>;<br/>


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