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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_1_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_1"><b>suppose </b></a><a NAME="E1:31_1_1_1_1"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c2">b</font> is <a href="polynom1.html#V1" title="POLYNOM1:attr.1">finite-support</a></span><br/><div class="add"><a NAME="E2:31_1_1_1_1"/>
 <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><b>hence </b><a NAME="E3:31_1_1_1_1"/>
 <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c2">b</font></span>)</span> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 <b>by </b><i><a class="txt" href="nat_3.html#E1:31_1_1_1_1"><i><font color="Green" title="E15">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="polynom1.html#D8" title="POLYNOM1:def.8">POLYNOM1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1_2"><b>suppose </b></a><a NAME="E1:31_1_1_1_2"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c2">b</font> is <a href="polynom1.html#V1" title="POLYNOM1:attr.1">finite-support</a></span><br/><div class="add"><a NAME="E2:31_1_1_1_2"/><b>then </b>
 <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <font color="Maroon" title="c2">b</font>
 <b>by </b><i><a class="ref" href="nat_3.html#T16" target="_self" title="NAT_3:th.16">Th16</a></i>;<br/><b>hence </b><a NAME="E3:31_1_1_1_2"/>
 <a href="polynom1.html#K10" title="POLYNOM1:func.10">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="nat_3.html#K4" title="NAT_3:func.4">*</a> <font color="Maroon" title="c2">b</font></span>)</span> 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" title="POLYNOM1:def.8">POLYNOM1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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