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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon">z0</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">z1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:49"/>
<font color="Maroon">z1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:49"/><b>then </b><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">z0</font>,<font color="Maroon">z1</font></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="txt" href="polynom5.html#E3:49"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E3:49"/><i><font color="Green">E34</font></i>: 
2 <a href="algseq_1.html#R1">is_at_least_length_of</a> <span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">z0</font>,<font color="Maroon">z1</font></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="algseq_1.html#D3">ALGSEQ_1:def 3</a><br/>

<b>assume </b><a NAME="E1:49_1"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 ;<br/>

<b>hence </b><a NAME="E2:49_1"/>
<span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">z0</font>,<font color="Maroon">z1</font></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">n</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="txt" href="polynom5.html#E3:49"><i><font color="Green">E34</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:49_2"/>
<font color="Maroon">n</font> <a href="algseq_1.html#R1">is_at_least_length_of</a> <span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">z0</font>,<font color="Maroon">z1</font></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span>
 ;<br/><a NAME="E2:49_2"/><b>then </b>
1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font>
 <b>by </b><i>, <a class="ref" href="algseq_1.html#D3">ALGSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E3:49_2"/>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:49"/>
 <a href="algseq_1.html#K3">len</a> <span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">z0</font>,<font color="Maroon">z1</font></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i>, <a class="ref" href="algseq_1.html#D4">ALGSEQ_1:def 4</a></i>;<br/>


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