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<a NAME="E1:50_1_1"/><i><font color="Green" title="E27">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
 
<b>by </b><i><a class="ref" href="hahnban1.html#D13" title="HAHNBAN1:def.13">HAHNBAN1:def 13</a></i>;<br/>
<a NAME="E2:50_1_1"/><i><font color="Green" title="E28">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:50_1_1_1"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/><b>thus </b><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">v</font> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
<b>by </b><i><a class="txt" href="vectsp10.html#E1:50_1_1"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="vectsp10.html#E2:50_1_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="vectsp10.html#E1:50_1_1_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="funct_1.html#D16" title="FUNCT_1:def.16">FUNCT_1:def 16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">v</font>
<b>by </b><i><a class="ref" href="hahnban1.html#T22" title="HAHNBAN1:th.22">HAHNBAN1:22</a></i>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:50_1_1_1"/>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:50_1_1"/><i><font color="Green" title="E29">A4</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:50_1_1_2"/><i><font color="Green" title="E30">A5</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font> )
 ;<br/><b>reconsider </b><font color="Maroon" title="c6">v</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c7">w</font> = <font color="Maroon" title="c5">y</font> as   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="txt" href="vectsp10.html#E1:50_1_1_2"><i><font color="Green" title="E30">A5</font></i></a></i>;<br/><b>thus </b><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">x</font> = 
<span class="p1">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">v</font>
<b>by </b><i><a class="txt" href="vectsp10.html#E4:50_1_1"><i><font color="Green" title="E29">A4</font></i></a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
<b>by </b><i><a class="ref" href="hahnban1.html#T22" title="HAHNBAN1:th.22">HAHNBAN1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">w</font>
<b>by </b><i><a class="ref" href="hahnban1.html#T22" title="HAHNBAN1:th.22">HAHNBAN1:22</a></i>
<br/>.= 
<font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">y</font>
<b>by </b><i><a class="txt" href="vectsp10.html#E4:50_1_1"><i><font color="Green" title="E29">A4</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:50_1_1"/>
<font color="Maroon" title="c3">f</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 <b>by </b><i><a class="ref" href="funct_1.html#D16" title="FUNCT_1:def.16">FUNCT_1:def 16</a></i>;<br/>


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