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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="vectsp_1.html#V10">degenerated</a>  <a href="vectsp_1.html#L2">multLoopStr_0</a> ;<br/>

<a NAME="E1:7"/>
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> 1 holds <br/><span class="p1">(<span class="default"><a href="polynom3.html#K13">1_.</a> <font color="Maroon">L</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>
 
<b>by </b><i><a class="ref" href="polynom3.html#T31">POLYNOM3:31</a></i>;<br/>
<a NAME="E2:7"/><b>then </b><i><font color="Green">E36</font></i>: 
1 <a href="algseq_1.html#R1">is_at_least_length_of</a>  <a href="polynom3.html#K13">1_.</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="algseq_1.html#D3">ALGSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_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><b>that </b><br/><a NAME="E1:7_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">i</font> <a href="algseq_1.html#R1">is_at_least_length_of</a>  <a href="polynom3.html#K13">1_.</a> <font color="Maroon">L</font>
 <b>and </b><br/><a NAME="E2:7_1"/><i><font color="Green">E38</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">i</font>
 ;<br/><a NAME="E3:7_1"/><i><font color="Green">E53</font></i>: 
 <a href="group_1.html#K2">1.</a> <font color="Maroon">L</font> <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="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/><a NAME="E4:7_1"/>
0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">i</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E5:7_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom3.html#K13">1_.</a> <font color="Maroon">L</font></span>)</span> <a href="normsp_1.html#K2">.</a> 0 <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#D3">ALGSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E6:7_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="polynom3.html#T31">POLYNOM3:31</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:7"/>
 <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K13">1_.</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="algseq_1.html#D4">ALGSEQ_1:def 4</a></i>;<br/>


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