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<b>set </b><font color="Maroon">f</font> = <font color="Maroon">m1</font> <a href="polynom8.html#K2" target="_self">*</a> <font color="Maroon">m2</font>;<br/>
<a NAME="E1:16_1_1"/>
 ex <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">n</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="polynom8.html#K2" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1"><b>proof </b></a><div class="add">

<b>take </b>
<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">m1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:16_1_1_1_1"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">m1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E2:16_1_1_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">m1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E3:16_1_1_1_1"/><b>then </b>
<font color="Maroon">m1</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="algseq_1.html#T22">ALGSEQ_1:22</a></i>;<br/><b>hence </b> <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> = 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">m2</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="polynom8.html#K2" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font>
<b>by </b><i/>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:16_1_1_1"/>
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">m1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/><span class="p1">(<span class="default"><font color="Maroon">m1</font> <a href="polynom8.html#K2" target="_self">*</a> <font color="Maroon">m2</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:16_1_1"/>
<font color="Maroon">m1</font> <a href="polynom8.html#K2" target="_self">*</a> <font color="Maroon">m2</font> is <a href="algseq_1.html#V1">finite-Support</a>
 <b>by </b><i><a class="ref" href="algseq_1.html#D2">ALGSEQ_1:def 2</a></i>;<br/>


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