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<b>reconsider </b><font color="Maroon">f</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font> <a href="funcop_1.html#K2">--&gt;</a> 0 as   <a href="hahnban.html#NM1">Functional</a> of <font color="Maroon">V</font> <b>by </b><i><a class="ref" href="funcop_1.html#T58">FUNCOP_1:58</a></i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban.html#D4" target="_self">HAHNBAN:def 4</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>, <font color="Maroon">y</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>thus </b><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">y</font></span>)</span> = 
0 <a href="real_1.html#K3">+</a> 0
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K3">+</a> 0
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban.html#D8" target="_self">HAHNBAN:def 8</a>
<div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>thus </b><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> 0
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">x</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="hahnban.html#D5" target="_self">HAHNBAN:def 5</a><br/><b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<b>thus </b><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font></span>)</span> = 
<font color="Maroon">r</font> <a href="real_1.html#K4">*</a> 0
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<font color="Maroon">r</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/>


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