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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a>  <a href="rlvect_1.html#L1" title="RLVECT_1:struct.1">LoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</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="c4">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>assume </b><b>that </b><br/><a NAME="E1:42"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c4">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>
 <b>and </b><br/><a NAME="E2:42"/><i><font color="Green" title="E30">A2</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="algseq_1.html#R1" title="ALGSEQ_1:pred.1">is_at_least_length_of</a> <font color="Maroon" title="c3">q</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">i</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> ; <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="E3:42"/>
<font color="Maroon" title="c5">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c4">n</font>
 ;<br/>

<a NAME="E4:42"/><b>then </b>
( <font color="Maroon" title="c2">p</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">L</font> &amp; <font color="Maroon" title="c3">q</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="txt" href="polynom3.html#E1:42"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="polynom3.html#E2:42"><i><font color="Green" title="E30">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><span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">i</font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D6" target="_self" title="POLYNOM3:def.6">Def6</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
;<br/><br/>


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