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<b>let </b><font color="Maroon">m</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:45"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">m</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<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">p</font> be   <a href="algseq_1.html#NM1">AlgSequence</a> of <font color="Maroon">L</font>;<br/>



<b>set </b><font color="Maroon">q</font> =  <a href="polynom8.html#K4" target="_self">mConv</a> <font color="Maroon">p</font>,<font color="Maroon">m</font>;<br/>
<b>thus </b><a NAME="E2:45"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom8.html#K4" target="_self">mConv</a> <font color="Maroon">p</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 <b>by </b><i>, <a class="ref" href="matrix_1.html#T24">MATRIX_1:24</a></i>;<br/>

<b>thus </b><a NAME="E3:45"/>
 <a href="matrix_1.html#K1">width</a> <span class="p1">(<span class="default"><a href="polynom8.html#K4" target="_self">mConv</a> <font color="Maroon">p</font>,<font color="Maroon">m</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="matrix_1.html#T24">MATRIX_1:24</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:45_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font>
 ;<br/><a NAME="E2:45_1"/><i><font color="Green">E39</font></i>: 
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:45_1"/>
<font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="polynom8.html#T2" target="_self">Th2</a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:45_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="polynom8.html#K4" target="_self">mConv</a> <font color="Maroon">p</font>,<font color="Maroon">m</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>,1 <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="polynom8.html#T3" target="_self">Th3</a>, </i>;<br/><b>hence </b><a NAME="E5:45_1"/>
<span class="p1">(<span class="default"><a href="polynom8.html#K4" target="_self">mConv</a> <font color="Maroon">p</font>,<font color="Maroon">m</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>,1 <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:45"/>
for <font color="Olive">i</font> being  <a href="nat_1.html#NM1">Nat</a>  st <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font> holds <br/><span class="p1">(<span class="default"><a href="polynom8.html#K4" target="_self">mConv</a> <font color="Maroon">p</font>,<font color="Maroon">m</font></span>)</span> <a href="matrix_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>,1 <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 ;<br/>


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