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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L2" title="STRUCT_0:struct.2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>





<b>thus </b><a NAME="E1:37"/>
( <font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> implies <font color="Maroon" title="c3">n</font> <a href="algseq_1.html#R1" title="ALGSEQ_1:pred.1">is_at_least_length_of</a> <font color="Maroon" title="c2">p</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:37_1"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="algseq_1.html#D3" title="ALGSEQ_1:def.3">ALGSEQ_1:def 3</a><br/>

<b>assume </b><a NAME="E2:37_1"/>
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">n</font>
 ;<br/>

<a NAME="E3:37_1"/><b>then </b>
<font color="Maroon" title="c4">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="polynom3.html#E1:37_1"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E4:37_1"/>
<font color="Maroon" title="c2">p</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">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/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:37"/>
<font color="Maroon" title="c3">n</font> <a href="algseq_1.html#R1" title="ALGSEQ_1:pred.1">is_at_least_length_of</a> <font color="Maroon" title="c2">p</font>
 ;<br/>

<b>hence </b><a NAME="E3:37"/>
<font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="ref" href="algseq_1.html#D4" title="ALGSEQ_1:def.4">ALGSEQ_1:def 4</a></i>;<br/>


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