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<b>let </b><font color="Maroon" title="c1">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="c2">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font>;<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">C</font>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>







<b>assume </b><a NAME="E1:64"/><i><font color="Green" title="E41">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="E2:64"/><b>then </b>
<font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K6" title="SEQ_1:func.6">+</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="rfunct_1.html#T66" target="_self" title="RFUNCT_1:th.66">Th66</a></i>;<br/>
<a NAME="E3:64"/><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="seq_1.html#K6" title="SEQ_1:func.6">+</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">C</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="E4:64"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K6" title="SEQ_1:func.6">+</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</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="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D3" title="SEQ_1:def.3">SEQ_1:def 3</a></i>;<br/>

<a NAME="E5:64"/>
<font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K7" title="SEQ_1:func.7">-</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="rfunct_1.html#E1:64"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="rfunct_1.html#T66" target="_self" title="RFUNCT_1:th.66">Th66</a></i>;<br/>
<a NAME="E6:64"/><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="seq_1.html#K7" title="SEQ_1:func.7">-</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">C</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="E7:64"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K7" title="SEQ_1:func.7">-</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</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="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D4" title="SEQ_1:def.4">SEQ_1:def 4</a></i>;<br/>

<a NAME="E8:64"/>
<font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</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="rfunct_1.html#E1:64"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="rfunct_1.html#T66" target="_self" title="RFUNCT_1:th.66">Th66</a></i>;<br/>
<a NAME="E9:64"/><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="seq_1.html#K8" title="SEQ_1:func.8">(#)</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">C</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="E10:64"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="seq_1.html#K8" title="SEQ_1:func.8">(#)</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</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="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c2">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D5" title="SEQ_1:def.5">SEQ_1:def 5</a></i>;<br/>


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