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<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">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">f2</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>;<br/>









<b>assume </b><a NAME="E1:41"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">f1</font> is <a href="partfun1.html#V1">total</a> &amp; <font color="Maroon">f2</font> is <a href="partfun1.html#V1">total</a> )
 ;<br/>

<a NAME="E2:41"/><b>then </b>
<font color="Maroon">f1</font> <a href="vfunct_1.html#K1" target="_self">+</a> <font color="Maroon">f2</font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i/>;<br/>
<a NAME="E3:41"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="vfunct_1.html#K1" target="_self">+</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:41"/>
<span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="vfunct_1.html#K1" target="_self">+</a> <font color="Maroon">f2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i/>;<br/>

<a NAME="E5:41"/>
<font color="Maroon">f1</font> <a href="vfunct_1.html#K2" target="_self">-</a> <font color="Maroon">f2</font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:41"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="vfunct_1.html#K2" target="_self">-</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:41"/>
<span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="vfunct_1.html#K2" target="_self">-</a> <font color="Maroon">f2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span>
 <b>by </b><i/>;<br/>


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