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<div class="add">

<b>set </b><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c2">m1</font> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <font color="Maroon" title="c3">m2</font>;<br/>
<a NAME="E1:16_1_1"/>
 ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>for <font color="Olive" title="b2">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b1">n</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <font color="Maroon" title="c3">m2</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b2">i</font> <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">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#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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" title="c5">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:16_1_1_1_1"/>
<font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><a NAME="E2:16_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">m1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:16_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">m1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">i</font> <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">L</font>
 <b>by </b><i><a class="ref" href="algseq_1.html#T22" title="ALGSEQ_1:th.22">ALGSEQ_1:22</a></i>;<br/><b>hence </b> <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">i</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">m2</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">i</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <font color="Maroon" title="c3">m2</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">i</font>
<b>by </b><i><a class="ref" href="polynom8.html#D2" target="_self" title="POLYNOM8:def.2">Def2</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:16_1_1_1"/>
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">m1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">m1</font> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <font color="Maroon" title="c3">m2</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Olive" title="b1">i</font> <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">L</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:16_1_1"/>
<font color="Maroon" title="c2">m1</font> <a href="polynom8.html#K2" title="POLYNOM8:func.2">*</a> <font color="Maroon" title="c3">m2</font> is <a href="algseq_1.html#V1" title="ALGSEQ_1:attr.1">finite-Support</a>
 <b>by </b><i><a class="ref" href="algseq_1.html#D2" title="ALGSEQ_1:def.2">ALGSEQ_1:def 2</a></i>;<br/>


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