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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">V</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">C</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">V</font>;<br/>







<b>assume </b><a NAME="E1:44"/><i><font color="Green" title="E19">A1</font></i>: 
<font color="Maroon" title="c4">f</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 ;<br/>

<a NAME="E2:44"/><b>then </b>
 <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">f</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 
<b>by </b><i><a class="ref" href="vfunct_1.html#T41" target="_self" title="VFUNCT_1:th.41">Th41</a></i>;<br/>
<a NAME="E3:44"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">f</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="E4:44"/>
<span class="p1">(<span class="default"><a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="vfunct_1.html#D6" target="_self" title="VFUNCT_1:def.6">Def6</a></i>;<br/>

<a NAME="E5:44"/>
<span class="p1"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">||.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">.||</a></span> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 
<b>by </b><i><a class="txt" href="vfunct_1.html#E1:44"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="vfunct_1.html#T42" target="_self" title="VFUNCT_1:th.42">Th42</a></i>;<br/>
<a NAME="E6:44"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">||.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">.||</a></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="E7:44"/>
<span class="p1"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">||.</a><span class="default"><font color="Maroon" title="c4">f</font></span><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="normsp_1.html#K1" title="NORMSP_1:func.1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c2">c</font></span>)</span></span><a href="normsp_1.html#K1" title="NORMSP_1:func.1">.||</a></span>
 <b>by </b><i><a class="ref" href="vfunct_1.html#D5" target="_self" title="VFUNCT_1:def.5">Def5</a></i>;<br/>


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