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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="realset2.html#V3">trivial</a> <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nfcont_1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:39"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="partfun1.html#V1">total</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a> )
 ;<br/>

<a NAME="E2:39"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="vfunct_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="ref" href="vfunct_1.html#T38">VFUNCT_1:38</a></i>;<br/>
<a NAME="E3:39"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vfunct_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<a NAME="E4:39"/><b>then </b>
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="vfunct_1.html#D1">VFUNCT_1:def 1</a></i>;<br/>
<a NAME="E5:39"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E6:39"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vfunct_1.html#K1">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nfcont_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nfcont_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="normsp_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nfcont_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nfcont_1.html#T19">NFCONT_1:19</a></i>;<br/>

<b>thus </b><a NAME="E7:39"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="vfunct_1.html#K2">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nfcont_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nfcont_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="normsp_1.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nfcont_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ndiff_1.html#E5:39"><i><font color="Green">E29</font></i></a>, <a class="ref" href="nfcont_1.html#T19">NFCONT_1:19</a></i>;<br/>


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