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<b>let </b><font color="Maroon" title="c1">M</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">V</font> be   <a href="clvect_1.html#NM5" title="CLVECT_1:NM.5">ComplexNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c5">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">M</font>;<br/>









<b>assume </b><a NAME="E1:41"/><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c3">f1</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <font color="Maroon" title="c4">f2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> )
 ;<br/>

<a NAME="E2:41"/><b>then </b>
<font color="Maroon" title="c3">f1</font> <a href="vfunct_2.html#K1" title="VFUNCT_2:func.1">+</a> <font color="Maroon" title="c4">f2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 
<b>by </b><i><a class="ref" href="vfunct_2.html#T32" target="_self" title="VFUNCT_2:th.32">Th32</a></i>;<br/>
<a NAME="E3:41"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="vfunct_2.html#K1" title="VFUNCT_2:func.1">+</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:41"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="vfunct_2.html#K1" title="VFUNCT_2:func.1">+</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="vfunct_2.html#D1" target="_self" title="VFUNCT_2:def.1">Def1</a></i>;<br/>

<a NAME="E5:41"/>
<font color="Maroon" title="c3">f1</font> <a href="vfunct_2.html#K2" title="VFUNCT_2:func.2">-</a> <font color="Maroon" title="c4">f2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 
<b>by </b><i><a class="txt" href="vfunct_2.html#E1:41"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="vfunct_2.html#T32" target="_self" title="VFUNCT_2:th.32">Th32</a></i>;<br/>
<a NAME="E6:41"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="vfunct_2.html#K2" title="VFUNCT_2:func.2">-</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:41"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="vfunct_2.html#K2" title="VFUNCT_2:func.2">-</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c5">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="vfunct_2.html#D2" target="_self" title="VFUNCT_2:def.2">Def2</a></i>;<br/>


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