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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> non <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  <a href="algstr_0.html#L5" title="ALGSTR_0:struct.5">multLoopStr_0</a> ;<br/>

<a NAME="E1:6"/>
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> 1 holds <br/><span class="p1">(<span class="default"><a href="polynom3.html#K10" title="POLYNOM3:func.10">1_.</a> <font color="Maroon" title="c1">L</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>
 
<b>by </b><i><a class="ref" href="polynom3.html#T31" title="POLYNOM3:th.31">POLYNOM3:31</a></i>;<br/>
<a NAME="E2:6"/><b>then </b><i><font color="Green" title="E5">A1</font></i>: 
1 <a href="algseq_1.html#R1" title="ALGSEQ_1:pred.1">is_at_least_length_of</a>  <a href="polynom3.html#K10" title="POLYNOM3:func.10">1_.</a> <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="algseq_1.html#D3" title="ALGSEQ_1:def.3">ALGSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:6_1"/><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c2">i</font> <a href="algseq_1.html#R1" title="ALGSEQ_1:pred.1">is_at_least_length_of</a>  <a href="polynom3.html#K10" title="POLYNOM3:func.10">1_.</a> <font color="Maroon" title="c1">L</font>
 <b>and </b><br/><a NAME="E2:6_1"/><i><font color="Green" title="E7">A3</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">i</font>
 ;<br/><a NAME="E3:6_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">i</font>
 <b>by </b><i><a class="txt" href="polynom4.html#E2:6_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:6_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom3.html#K10" title="POLYNOM3:func.10">1_.</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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="txt" href="polynom4.html#E1:6_1"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="algseq_1.html#D3" title="ALGSEQ_1:def.3">ALGSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E5:6_1"/>
contradiction
 <b>by </b><i><a class="ref" href="polynom3.html#T31" title="POLYNOM3:th.31">POLYNOM3:31</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:6"/>
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K10" title="POLYNOM3:func.10">1_.</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="polynom4.html#E2:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="algseq_1.html#D4" title="ALGSEQ_1:def.4">ALGSEQ_1:def 4</a></i>;<br/>


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