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<b>set </b><font color="Maroon" title="c2">f</font> = <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ;<br/>
<a NAME="E1:81_1_1"/><i><font color="Green" title="E42">A1</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c3">f</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:81_1_1_1"/>
 <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><b>then consider </b><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:81_1_1_1"/><i><font color="Green" title="E43">A3</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><a NAME="E4:81_1_1_1"/><i><font color="Green" title="E44">A4</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="polynom1.html#E3:81_1_1_1"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="polynom1.html#D7" target="_self" title="POLYNOM1:def.7">Def7</a></i>;<br/><a NAME="E5:81_1_1_1"/>
 <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="polynom1.html#T41" target="_self" title="POLYNOM1:th.41">Th41</a></i>;<br/><b>hence </b><a NAME="E6:81_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polynom1.html#E1:81_1_1"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="polynom1.html#E3:81_1_1_1"><i><font color="Green" title="E43">A3</font></i></a>, <a class="txt" href="polynom1.html#E4:81_1_1_1"><i><font color="Green" title="E44">A4</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:81_1_1"/>
 <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c3">f</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="polynom1.html#D8" target="_self" title="POLYNOM1:def.8">POLYNOM1:def 8</a><br/>


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