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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C</font> being 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/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">C</font>, <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>   st <font color="Olive" title="b2">f1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c1">X</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Olive" title="b3">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">f1</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Olive" title="b3">f2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><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></span>)</span> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a></span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <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>   st <font color="Olive" title="b1">f1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c1">X</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Olive" title="b2">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Olive" title="b2">f2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><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></span>)</span> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a></span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">f1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c1">X</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Maroon" title="c5">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><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></span>)</span> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> )</span><br/>









<b>assume </b><a NAME="E1:81"/><i><font color="Green" title="E53">A1</font></i>: 
( <font color="Maroon" title="c4">f1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c1">X</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a> &amp; <font color="Maroon" title="c5">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><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></span>)</span> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a></span><br/>

<a NAME="E2:81"/><b>then </b>
<font color="Maroon" title="c5">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">Y</font> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T93" target="_self" title="CFUNCT_1:th.93">Th93</a></i>;<br/>
<b>hence </b><a NAME="E3:81"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f1</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Maroon" title="c5">f2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><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></span>)</span> is <a href="seq_2.html#V3" title="SEQ_2:attr.3">bounded</a>
 <b>by </b><i><a class="txt" href="#E1:81"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="cfunct_1.html#T87" target="_self" title="CFUNCT_1:th.87">Th87</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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