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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a> <a href="vectsp_1.html#V7">distributive</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">L</font>, <font color="Maroon">q</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">L</font>, <font color="Maroon">r</font> be   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">L</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>consider </b><font color="Maroon">r1</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E2:62_1"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E3:62_1"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">q</font></span>)</span> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r1</font>
 <b>and </b><br/><a NAME="E4:62_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r1</font> holds <br/><font color="Maroon">r1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">q</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Olive">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Olive">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E4:62_1"><i><font color="Green">E36</font></i></a></i>;<br/><b>consider </b><font color="Maroon">r2</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E6:62_1"/><i><font color="Green">E43</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E7:62_1"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r2</font>
 <b>and </b><br/><a NAME="E8:62_1"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r2</font> holds <br/><font color="Maroon">r2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Olive">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Olive">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E4:62_1"><i><font color="Green">E36</font></i></a></i>;<br/><b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ) <b>-&gt; </b>   <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_2.html#K3">*</a>  = <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>;<br/><b>consider </b><font color="Maroon">f2</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E10:62_1"/><i><font color="Green">E46</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E11:62_1"/><i><font color="Green">E64</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> holds <br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">k</font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1">FINSEQ_2:sch 1</a>();<br/></i><b>reconsider </b><font color="Maroon">f2</font> = <font color="Maroon">f2</font> as    <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_2.html#K3">*</a>  ;<br/><b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ) <b>-&gt; </b>   <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_2.html#K3">*</a>  = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>,2</span>)</span>;<br/><b>consider </b><font color="Maroon">g2</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E14:62_1"/><i><font color="Green">E65</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E15:62_1"/><i><font color="Green">E67</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> holds <br/><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">k</font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1">FINSEQ_2:sch 1</a>();<br/></i><b>reconsider </b><font color="Maroon">g2</font> = <font color="Maroon">g2</font> as    <a href="finseq_1.html#M2">FinSequence</a> of <span class="p1">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_2.html#K3">*</a>  ;<br/><b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ) <b>-&gt; </b>   <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="finseq_2.html#K3">*</a>  =  <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">f1</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E18:62_1"/><i><font color="Green">E68</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font>
 <b>and </b><br/><a NAME="E19:62_1"/><i><font color="Green">E69</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font></span>)</span> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">k</font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1">FINSEQ_2:sch 1</a>();<br/></i><b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ) <b>-&gt; </b>   <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="finseq_2.html#K3">*</a>  =  <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span>;<br/><b>consider </b><font color="Maroon">g1</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E21:62_1"/><i><font color="Green">E70</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font>
 <b>and </b><br/><a NAME="E22:62_1"/><i><font color="Green">E71</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font></span>)</span> holds <br/><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">k</font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1">FINSEQ_2:sch 1</a>();<br/></i><a NAME="E23:62_1"/><i><font color="Green">E72</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="matrlin.html#D8">MATRLIN:def 8</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_1"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E2:62_1_1"/><b>then </b><i><font color="Green">E74</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r1</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:62_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i><a class="ref" href="matrlin.html#D8">MATRLIN:def 8</a></i>;<br/><a NAME="E4:62_1_1"/><b>then </b><i><font color="Green">E80</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E5:62_1_1"/><i><font color="Green">E81</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f1</font>
 <b>by </b><i>, <a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E6:62_1_1"/><i><font color="Green">E91</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font>
 <b>by </b><i>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><b>consider </b><font color="Maroon">r3</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E8:62_1_1"/><i><font color="Green">E92</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r3</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E9:62_1_1"/><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">q</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r3</font>
 <b>and </b><br/><a NAME="E10:62_1_1"/><i><font color="Green">E94</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r3</font> holds <br/><font color="Maroon">r3</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Olive">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Olive">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E4:62_1"><i><font color="Green">E36</font></i></a></i>;<br/><i><font color="Green">E102</font></i>: <font color="Maroon">f1</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font> = 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
 <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, , </i>
;<br/><a NAME="E12:62_1_1"/><i><font color="Green">E103</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/> <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i/>
<br/>.= 
<font color="Maroon">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E11:62_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>
;<br/><a NAME="E14:62_1_1"/><b>then </b><i><font color="Green">E104</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E15:62_1_1"/><i><font color="Green">E105</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><i><font color="Green">E106</font></i>: <font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font> = 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i>, , <a class="ref" href="polynom3.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i>, </i>
;<br/><b>then </b><i><font color="Green">E107</font></i>:  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E14:62_1"><i><font color="Green">E65</font></i></a>, </i>
;<br/><i><font color="Green">E109</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
;<br/><a NAME="E19:62_1_1"/><i><font color="Green">E110</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">r3</font> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r3</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D3">POLYNOM1:def 3</a></i>;<br/><a NAME="E20:62_1_1"/><b>then </b><i><font color="Green">E111</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">r3</font> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">r3</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E21:62_1_1"/><i><font color="Green">E114</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="txt" href="polynom3.html#E11:62_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_1_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_1_6"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
 ;<br/><a NAME="E2:62_1_1_6"/><b>then </b><i><font color="Green">E116</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r3</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E23:62_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><i><font color="Green">E117</font></i>: <font color="Maroon">r3</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font> = 
<font color="Maroon">r3</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T5" target="_self">Th5</a>, <a class="txt" href="polynom3.html#E2:62_1_1"><i><font color="Green">E74</font></i></a></i>
;<br/><i><font color="Green">E118</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="polynom3.html#E1:62_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E15:62_1"><i><font color="Green">E67</font></i></a>, <a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="polynom3.html#E1:62_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i>, <a class="txt" href="polynom3.html#E23:62_1"><i><font color="Green">E72</font></i></a>, <a class="txt" href="polynom3.html#E1:62_1_1"><i><font color="Green">E73</font></i></a>, </i>
<br/>.= 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom3.html#E1:62_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><a NAME="E5:62_1_1_6"/>
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 3 &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 3 &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 3 )
 <b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a></i>;<br/><a NAME="E6:62_1_1_6"/><b>then </b>
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/><a NAME="E7:62_1_1_6"/><b>then </b><i><font color="Green">E119</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><i><font color="Green">E120</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 1
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1
<b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><i><font color="Green">E121</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 2
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><i><font color="Green">E168</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 3
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="polynom3.html#E1:62_1_1"><i><font color="Green">E73</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">r3</font> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="txt" href="polynom3.html#E2:62_1_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="polynom3.html#T6" target="_self">Th6</a>, , , <a class="txt" href="polynom3.html#E4:62_1_1"><i><font color="Green">E80</font></i></a>, <a class="ref" href="polynom1.html#D3">POLYNOM1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">r3</font> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="txt" href="polynom3.html#E21:62_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polynom3.html#E2:62_1_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/></div><b>end;</b></div><a NAME="E23:62_1_1"/><b>then </b><i><font color="Green">E169</font></i>: 
 <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">r3</font> <a href="polynom1.html#K7">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E19:62_1"><i><font color="Green">E69</font></i></a>, <a class="txt" href="polynom3.html#E22:62_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="polynom3.html#E23:62_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><a NAME="E24:62_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">q</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">r3</font> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom3.html#D2" target="_self">Def2</a>, <a class="ref" href="polynom1.html#T29">POLYNOM1:29</a></i>;<br/><b>hence </b><font color="Maroon">r1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
 <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">r3</font> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T4" target="_self">Th4</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">f1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">j</font>
<b>by </b><i>, , , , <a class="txt" href="polynom3.html#E1:62_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="matrlin.html#D8">MATRLIN:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">f1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i>, , , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><br/></div><b>end;</b></div><a NAME="E25:62_1"/><b>then </b>
<font color="Maroon">r1</font> <a href="hidden.html#R1">=</a>  <a href="matrlin.html#K8">Sum</a> <font color="Maroon">f1</font>
 <b>by </b><i>, , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><a NAME="E26:62_1"/><b>then </b><i><font color="Green">E170</font></i>: 
 <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T34">POLYNOM1:34</a></i>;<br/><a NAME="E27:62_1"/><i><font color="Green">E171</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">g1</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, , <a class="ref" href="matrlin.html#D8">MATRLIN:def 8</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_2"/><i><font color="Green">E172</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E2:62_1_2"/><b>then </b><i><font color="Green">E173</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r2</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E6:62_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:62_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="matrlin.html#D8">MATRLIN:def 8</a></i>;<br/><a NAME="E4:62_1_2"/><b>then </b><i><font color="Green">E174</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E5:62_1_2"/><i><font color="Green">E175</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g1</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E6:62_1"><i><font color="Green">E43</font></i></a>, , , <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E6:62_1_2"/><i><font color="Green">E176</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 <b>by </b><i>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><b>consider </b><font color="Maroon">r3</font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E8:62_1_2"/><i><font color="Green">E177</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r3</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E9:62_1_2"/><i><font color="Green">E178</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r3</font>
 <b>and </b><br/><a NAME="E10:62_1_2"/><i><font color="Green">E179</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r3</font> holds <br/><font color="Maroon">r3</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Olive">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Olive">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E4:62_1"><i><font color="Green">E36</font></i></a></i>;<br/><i><font color="Green">E180</font></i>: <font color="Maroon">g1</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font> = 
<font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
 <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, , </i>
;<br/><a NAME="E12:62_1_2"/><i><font color="Green">E181</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E13:62_1_2"/><b>then </b><i><font color="Green">E182</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E14:62_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E15:62_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E16:62_1_2"/><b>then </b><i><font color="Green">E183</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><i><font color="Green">E184</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="txt" href="polynom3.html#E15:62_1"><i><font color="Green">E67</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><a NAME="E18:62_1_2"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>,2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font>
 <b>by </b><i/>;<br/><a NAME="E19:62_1_2"/><b>then </b><i><font color="Green">E185</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>,2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E20:62_1_2"/><i><font color="Green">E186</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><i><font color="Green">E187</font></i>: <font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font> = 
<font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i>, , <a class="ref" href="polynom3.html#D2" target="_self">Def2</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>,2</span>)</span>
<b>by </b><i>, </i>
;<br/><b>then </b><i><font color="Green">E188</font></i>:  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>,2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E21:62_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polynom3.html#E22:62_1"><i><font color="Green">E71</font></i></a></i>
;<br/><i><font color="Green">E189</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
;<br/><a NAME="E24:62_1_2"/><i><font color="Green">E190</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K6">*</a> <font color="Maroon">r3</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r3</font>
 <b>by </b><i><a class="ref" href="polynom1.html#D2">POLYNOM1:def 2</a></i>;<br/><a NAME="E25:62_1_2"/><b>then </b><i><font color="Green">E191</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K6">*</a> <font color="Maroon">r3</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">r3</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_2_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_2_6"/><i><font color="Green">E192</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>
 ;<br/><a NAME="E2:62_1_2_6"/><b>then </b><i><font color="Green">E193</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r3</font>
 <b>by </b><i><a class="ref" href="polynom3.html#T5" target="_self">Th5</a>, <a class="txt" href="polynom3.html#E19:62_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><i><font color="Green">E194</font></i>: <font color="Maroon">r3</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font> = 
<font color="Maroon">r3</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E11:62_1"><i><font color="Green">E64</font></i></a>, </i>
;<br/><i><font color="Green">E195</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E23:62_1"><i><font color="Green">E72</font></i></a>, , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom3.html#E19:62_1"><i><font color="Green">E69</font></i></a>, , </i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><a NAME="E5:62_1_2_6"/>
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 3 &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 3 &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 3 )
 <b>by </b><i><a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a></i>;<br/><a NAME="E6:62_1_2_6"/><b>then </b>
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span> )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/><a NAME="E7:62_1_2_6"/><b>then </b><i><font color="Green">E196</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then </b><i><font color="Green">E197</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 1
<b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1
<b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><i><font color="Green">E198</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 2
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1
<b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><i><font color="Green">E199</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 3
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 3</span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K6">*</a> <font color="Maroon">r3</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font>
<b>by </b><i>, , <a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, <a class="ref" href="polynom3.html#D3" target="_self">Def3</a>, , <a class="ref" href="polynom1.html#D2">POLYNOM1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K6">*</a> <font color="Maroon">r3</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i><a class="ref" href="polynom3.html#T6" target="_self">Th6</a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/></div><b>end;</b></div><a NAME="E27:62_1_2"/><b>then </b><i><font color="Green">E200</font></i>: 
 <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K6">*</a> <font color="Maroon">r3</font>
 <b>by </b><i><a class="ref" href="polynom3.html#T5" target="_self">Th5</a>, <a class="txt" href="polynom3.html#E19:62_1"><i><font color="Green">E69</font></i></a>, , , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><a NAME="E28:62_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K6">*</a> <font color="Maroon">r3</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T28">POLYNOM1:28</a></i>;<br/><b>hence </b><font color="Maroon">r2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
 <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K6">*</a> <font color="Maroon">r3</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E8:62_1"><i><font color="Green">E45</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">g1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">j</font>
<b>by </b><i>, <a class="ref" href="polynom3.html#D1" target="_self">Def1</a>, , <a class="txt" href="polynom3.html#E14:62_1"><i><font color="Green">E65</font></i></a>, , <a class="ref" href="matrlin.html#D8">MATRLIN:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin.html#K8">Sum</a> <font color="Maroon">g1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i>, <a class="ref" href="polynom3.html#D1" target="_self">Def1</a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><br/></div><b>end;</b></div><a NAME="E29:62_1"/><b>then </b>
<font color="Maroon">r2</font> <a href="hidden.html#R1">=</a>  <a href="matrlin.html#K8">Sum</a> <font color="Maroon">g1</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E6:62_1"><i><font color="Green">E43</font></i></a>, , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><a NAME="E30:62_1"/><b>then </b><i><font color="Green">E201</font></i>: 
 <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T34">POLYNOM1:34</a></i>;<br/><a NAME="E31:62_1"/><i><font color="Green">E202</font></i>: 
(  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f1</font> &amp;  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font> )
 <b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>;<br/><a NAME="E32:62_1"/><b>then </b><i><font color="Green">E203</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f1</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_3"/><i><font color="Green">E204</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E2:62_1_3"/><b>then </b><i><font color="Green">E205</font></i>: 
( <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f1</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font> )
 <b>by </b><i><a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:62_1_3"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a>  <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, , </i>;<br/><b>then </b><i><font color="Green">E206</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D2" target="_self">Def2</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">j</font> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D2" target="_self">Def2</a>, <a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f1</font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">j</font>
<b>by </b><i><a class="ref" href="polynom3.html#D2" target="_self">Def2</a>, <a class="ref" href="polynom3.html#T5" target="_self">Th5</a>, <a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
;<br/></div><b>end;</b></div><a NAME="E34:62_1"/><b>then </b><i><font color="Green">E207</font></i>: 
 <a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K5">Card</a> <font color="Maroon">f1</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="polynom3.html#D1" target="_self">Def1</a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><a NAME="E35:62_1"/><b>then </b><i><font color="Green">E208</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T31">POLYNOM1:31</a></i>;<br/><a NAME="E36:62_1"/><b>then </b><i><font color="Green">E209</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E37:62_1"/><i><font color="Green">E210</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_4"/><i><font color="Green">E211</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:62_1_4"/><b>then </b>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then consider </b><font color="Maroon">i1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:62_1_4"/><i><font color="Green">E212</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f1</font>
 <b>and </b><br/><a NAME="E5:62_1_4"/><i><font color="Green">E213</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
 <b>and </b><br/><a NAME="E6:62_1_4"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 <b>and </b><br/><a NAME="E7:62_1_4"/><i><font color="Green">E215</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T32">POLYNOM1:32</a></i>;<br/><a NAME="E8:62_1_4"/><i><font color="Green">E216</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">f2</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="polynom3.html#E14:62_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E9:62_1_4"/><b>then </b><i><font color="Green">E217</font></i>: 
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E10:62_1_4"/><i><font color="Green">E218</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E19:62_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/> <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E21:62_1"><i><font color="Green">E70</font></i></a>, </i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i>, , <a class="txt" href="polynom3.html#E14:62_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><a NAME="E12:62_1_4"/><b>then </b>
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E13:62_1_4"/><b>then </b><i><font color="Green">E219</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E22:62_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E14:62_1_4"/><b>then </b><i><font color="Green">E220</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E15:62_1_4"/><i><font color="Green">E221</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E16:62_1_4"/><i><font color="Green">E222</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom3.html#D2" target="_self">Def2</a>, <a class="txt" href="polynom3.html#E11:62_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then consider </b><font color="Maroon">i2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E18:62_1_4"/><i><font color="Green">E223</font></i>: 
<font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font>
 <b>and </b><br/><a NAME="E19:62_1_4"/><i><font color="Green">E224</font></i>: 
<font color="Maroon">j2</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span>
 <b>and </b><br/><a NAME="E20:62_1_4"/><i><font color="Green">E225</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j2</font>
 <b>and </b><br/><a NAME="E21:62_1_4"/><i><font color="Green">E226</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T32">POLYNOM1:32</a></i>;<br/><span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f1</font></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font> = 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f1</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j2</font>
<b>by </b><i><a class="txt" href="polynom3.html#E15:62_1"><i><font color="Green">E67</font></i></a>, , </i>
;<br/><a NAME="E23:62_1_4"/><b>then </b><i><font color="Green">E227</font></i>: 
( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> &amp; <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> )
 <b>by </b><i>, <a class="txt" href="polynom3.html#E14:62_1"><i><font color="Green">E65</font></i></a>, , , , </i>;<br/><i><font color="Green">E228</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j1</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font>
<b>by </b><i><a class="txt" href="polynom3.html#E22:62_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font>
<b>by </b><i><a class="ref" href="polynom3.html#T6" target="_self">Th6</a>, , , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="polynom3.html#E21:62_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polynom3.html#E23:62_1"><i><font color="Green">E72</font></i></a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i><a class="ref" href="polynom3.html#D2" target="_self">Def2</a>, , <a class="txt" href="polynom3.html#E11:62_1"><i><font color="Green">E64</font></i></a>, , </i>
;<br/></div><b>end;</b></div><a NAME="E39:62_1"/><b>then </b><i><font color="Green">E229</font></i>: 
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom3.html#T5" target="_self">Th5</a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><a NAME="E40:62_1"/><i><font color="Green">E230</font></i>: 
(  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g1</font> &amp;  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font> )
 <b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>;<br/><a NAME="E41:62_1"/><b>then </b><i><font color="Green">E231</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g1</font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_5"/><i><font color="Green">E232</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E2:62_1_5"/><b>then </b><i><font color="Green">E233</font></i>: 
( <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g1</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font> )
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:62_1_5"/>
<font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a>  <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span>
 <b>by </b><i>, , <a class="txt" href="polynom3.html#E15:62_1"><i><font color="Green">E67</font></i></a></i>;<br/><b>then </b><i><font color="Green">E234</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">j</font> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g1</font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="polynom3.html#E19:62_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
;<br/></div><b>end;</b></div><a NAME="E43:62_1"/><b>then </b><i><font color="Green">E235</font></i>: 
 <a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K5">Card</a> <font color="Maroon">g1</font>
 <b>by </b><i>, , , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><a NAME="E44:62_1"/><b>then </b><i><font color="Green">E236</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T31">POLYNOM1:31</a></i>;<br/><a NAME="E45:62_1"/><b>then </b><i><font color="Green">E237</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E46:62_1"/><i><font color="Green">E238</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E47:62_1"/><i><font color="Green">E239</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, </i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_6"/><i><font color="Green">E240</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:62_1_6"/><b>then </b>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then consider </b><font color="Maroon">i1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:62_1_6"/><i><font color="Green">E241</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g1</font>
 <b>and </b><br/><a NAME="E5:62_1_6"/><i><font color="Green">E242</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
 <b>and </b><br/><a NAME="E6:62_1_6"/><i><font color="Green">E243</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 <b>and </b><br/><a NAME="E7:62_1_6"/><i><font color="Green">E244</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T32">POLYNOM1:32</a></i>;<br/><a NAME="E8:62_1_6"/><i><font color="Green">E245</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E9:62_1_6"/><b>then </b><i><font color="Green">E246</font></i>: 
<font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E10:62_1_6"/><i><font color="Green">E247</font></i>: 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E11:62_1_6"/><i><font color="Green">E248</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/> <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E14:62_1"><i><font color="Green">E65</font></i></a>, <a class="txt" href="polynom3.html#E15:62_1"><i><font color="Green">E67</font></i></a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><a NAME="E13:62_1_6"/><b>then </b>
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E14:62_1_6"/><b>then </b><i><font color="Green">E249</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E15:62_1_6"/><b>then </b><i><font color="Green">E250</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E16:62_1_6"/><i><font color="Green">E251</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E18:62_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="polynom3.html#E23:62_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>then consider </b><font color="Maroon">i2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E18:62_1_6"/><i><font color="Green">E252</font></i>: 
<font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 <b>and </b><br/><a NAME="E19:62_1_6"/><i><font color="Green">E253</font></i>: 
<font color="Maroon">j2</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span>
 <b>and </b><br/><a NAME="E20:62_1_6"/><i><font color="Green">E254</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g2</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j2</font>
 <b>and </b><br/><a NAME="E21:62_1_6"/><i><font color="Green">E255</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T32">POLYNOM1:32</a></i>;<br/><span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g1</font></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font> = 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j2</font>
<b>by </b><i><a class="ref" href="polynom3.html#T6" target="_self">Th6</a>, , </i>
;<br/><a NAME="E23:62_1_6"/><b>then </b><i><font color="Green">E256</font></i>: 
( <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> &amp; <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> )
 <b>by </b><i><a class="txt" href="polynom3.html#E15:62_1"><i><font color="Green">E67</font></i></a>, , , , , </i>;<br/><i><font color="Green">E257</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j1</font> = 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font>
<b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j</font>
<b>by </b><i><a class="ref" href="polynom3.html#D3" target="_self">Def3</a>, , , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">g2</font> <a href="polynom1.html#K3">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="polynom1.html#K3">/.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 3</span>)</span></span>)</span>
<b>by </b><i>, , , , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p2">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
<b>by </b><i><a class="txt" href="polynom3.html#E19:62_1"><i><font color="Green">E69</font></i></a>, <a class="txt" href="polynom3.html#E21:62_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polynom3.html#E23:62_1"><i><font color="Green">E72</font></i></a>, , </i>
;<br/></div><b>end;</b></div><a NAME="E49:62_1"/><b>then </b><i><font color="Green">E258</font></i>: 
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a>  <a href="polynom3.html#K7" target="_self">prodTuples</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font>,<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom3.html#E22:62_1"><i><font color="Green">E71</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_7"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>thus </b><a NAME="E1:62_1_7"/>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> implies <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_7_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:62_1_7_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:62_1_7_1"/><i><font color="Green">E259</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span>
 <b>and </b><br/><a NAME="E4:62_1_7_1"/><i><font color="Green">E260</font></i>: 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/>
<b>consider </b><font color="Maroon">i1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E6:62_1_7_1"/><i><font color="Green">E261</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font>
 <b>and </b><br/><a NAME="E7:62_1_7_1"/><i><font color="Green">E262</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
 <b>and </b><br/><a NAME="E8:62_1_7_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 <b>and </b><br/><a NAME="E9:62_1_7_1"/><i><font color="Green">E263</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T32">POLYNOM1:32</a></i>;<br/>
<a NAME="E10:62_1_7_1"/><i><font color="Green">E264</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="polynom3.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E11:62_1_7_1"/><b>then </b><i><font color="Green">E265</font></i>: 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E12:62_1_7_1"/><b>then </b>
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>;<br/>
<a NAME="E13:62_1_7_1"/><b>then </b>
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E14:62_1_7_1"/><b>then </b><i><font color="Green">E266</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">i1</font>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E15:62_1_7_1"/><i><font color="Green">E267</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i1</font> &amp; <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E16:62_1_7_1"/><b>then </b><i><font color="Green">E268</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/>
<i><font color="Green">E269</font></i>: <font color="Maroon">y</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span>
<b>by </b><i>, , , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, </i>
<br/>.= 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/>
<b>set </b><font color="Maroon">i2</font> = <font color="Maroon">j1</font>;<br/>
<b>set </b><font color="Maroon">j2</font> = <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1;<br/>
<a NAME="E18:62_1_7_1"/><i><font color="Green">E270</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j1</font> &amp; <font color="Maroon">j1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i1</font> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E19:62_1_7_1"/><b>then </b><i><font color="Green">E271</font></i>: 
( <font color="Maroon">j1</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">i1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E20:62_1_7_1"/><i><font color="Green">E272</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j1</font>
 
<b>by </b><i>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E21:62_1_7_1"/><b>then </b><i><font color="Green">E273</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E22:62_1_7_1"/><i><font color="Green">E274</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<a NAME="E23:62_1_7_1"/><i><font color="Green">E275</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E24:62_1_7_1"/><b>then </b><i><font color="Green">E276</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E25:62_1_7_1"/><i><font color="Green">E277</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E26:62_1_7_1"/>
<font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font>
 
<b>by </b><i>, <a class="ref" href="jordan3.html#T5">JORDAN3:5</a></i>;<br/>
<a NAME="E27:62_1_7_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E28:62_1_7_1"/><b>then </b><i><font color="Green">E278</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<i><font color="Green">E279</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font>

;<br/>
<a NAME="E30:62_1_7_1"/><b>then </b><i><font color="Green">E280</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E31:62_1_7_1"/><i><font color="Green">E281</font></i>: 
<font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>,2</span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E32:62_1_7_1"/><i><font color="Green">E282</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>,2</span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>,2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/>
<a NAME="E34:62_1_7_1"/><b>then </b>
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom3.html#D4" target="_self">Def4</a>, , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>;<br/>
<a NAME="E35:62_1_7_1"/><b>then </b><i><font color="Green">E283</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<a NAME="E36:62_1_7_1"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font>
 
<b>by </b><i>, <a class="ref" href="jordan3.html#T5">JORDAN3:5</a></i>;<br/>
<a NAME="E37:62_1_7_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E38:62_1_7_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<b>then </b><i><font color="Green">E284</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/>
<i><font color="Green">E285</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D4" target="_self">Def4</a>, , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/>
<a NAME="E41:62_1_7_1"/>
( <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g2</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p4">(<span class="default"><font color="Maroon">g2</font> <a href="finseq_1.html#K17">|</a> <span class="p5">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 
<b>by </b><i>, , <a class="ref" href="polynom1.html#T33">POLYNOM1:33</a></i>;<br/>
<b>hence </b><a NAME="E42:62_1_7_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom3.html#D3" target="_self">Def3</a>, <a class="ref" href="polynom3.html#T8" target="_self">Th8</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>


</div><b>end;</b></div><b>assume </b><a NAME="E2:62_1_7"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:62_1_7"/><i><font color="Green">E286</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
 <b>and </b><br/><a NAME="E5:62_1_7"/><i><font color="Green">E287</font></i>: 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/><b>consider </b><font color="Maroon">i1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E7:62_1_7"/><i><font color="Green">E288</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 <b>and </b><br/><a NAME="E8:62_1_7"/><i><font color="Green">E289</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
 <b>and </b><br/><a NAME="E9:62_1_7"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g2</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 <b>and </b><br/><a NAME="E10:62_1_7"/><i><font color="Green">E290</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T32">POLYNOM1:32</a></i>;<br/><a NAME="E11:62_1_7"/><i><font color="Green">E291</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom3.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E12:62_1_7"/><b>then </b><i><font color="Green">E292</font></i>: 
<font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span>
 <b>by </b><i/>;<br/><a NAME="E13:62_1_7"/><b>then </b>
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finsop_1.html#K5">dom</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>;<br/><a NAME="E14:62_1_7"/><b>then </b>
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E15:62_1_7"/><b>then </b><i><font color="Green">E293</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><a NAME="E16:62_1_7"/><i><font color="Green">E294</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i1</font> &amp; <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E17:62_1_7"/><b>then </b><i><font color="Green">E295</font></i>: 
( <font color="Maroon">i1</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><b>then </b><i><font color="Green">E296</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>

;<br/><a NAME="E19:62_1_7"/><i><font color="Green">E297</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom3.html#D3" target="_self">Def3</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><i><font color="Green">E298</font></i>: <font color="Maroon">y</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span>
<b>by </b><i>, , , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><b>set </b><font color="Maroon">i2</font> = <span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font>;<br/><b>set </b><font color="Maroon">j2</font> = <font color="Maroon">i1</font>;<br/><a NAME="E21:62_1_7"/><i><font color="Green">E299</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E22:62_1_7"/><b>then </b><i><font color="Green">E300</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E23:62_1_7"/>
<font color="Maroon">j1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E24:62_1_7"/><b>then </b><i><font color="Green">E301</font></i>: 
<font color="Maroon">j1</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E25:62_1_7"/><i><font color="Green">E302</font></i>: 
<font color="Maroon">j1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E26:62_1_7"/><b>then </b>
<font color="Maroon">j1</font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E27:62_1_7"/><b>then </b>
<font color="Maroon">j1</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E28:62_1_7"/><b>then </b><i><font color="Green">E303</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E29:62_1_7"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E30:62_1_7"/><b>then </b><i><font color="Green">E304</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E31:62_1_7"/><b>then </b><i><font color="Green">E305</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E32:62_1_7"/><i><font color="Green">E306</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E33:62_1_7"/><b>then </b><i><font color="Green">E307</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>;<br/><a NAME="E34:62_1_7"/><i><font color="Green">E308</font></i>: 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i>, </i>;<br/><a NAME="E35:62_1_7"/><i><font color="Green">E309</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/> <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>
;<br/><a NAME="E37:62_1_7"/><b>then </b>
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom3.html#D4" target="_self">Def4</a>, , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>;<br/><a NAME="E38:62_1_7"/><b>then </b><i><font color="Green">E310</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E39:62_1_7"/><i><font color="Green">E311</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E40:62_1_7"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i1</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E41:62_1_7"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><b>then </b><i><font color="Green">E312</font></i>: <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j1</font>
<b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><i><font color="Green">E313</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D4" target="_self">Def4</a>, , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom3.html#T8" target="_self">Th8</a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/><a NAME="E44:62_1_7"/>
( <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f2</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="finseq_1.html#K17">|</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">i1</font></span>)</span> )
 <b>by </b><i>, , <a class="ref" href="polynom1.html#T33">POLYNOM1:33</a></i>;<br/><b>hence </b><a NAME="E45:62_1_7"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom3.html#T9" target="_self">Th9</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><a NAME="E51:62_1"/><b>then </b><i><font color="Green">E314</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/><i><font color="Green">E315</font></i>:  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span> = 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font>
<b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom3.html#E10:62_1"><i><font color="Green">E46</font></i></a>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
<br/>.= 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_5.html#T60">FINSEQ_5:60</a></i>
;<br/><a NAME="E53:62_1"/><b>then </b><i><font color="Green">E316</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">j</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:62_1_9"/>
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:62_1_9"/><b>then </b><i><font color="Green">E317</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:62_1_9"/><b>then </b><i><font color="Green">E318</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>;<br/><a NAME="E4:62_1_9"/><i><font color="Green">E319</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 <b>by </b><i><a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>;<br/><a NAME="E5:62_1_9"/><b>then </b><i><font color="Green">E320</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E6:62_1_9"/><i><font color="Green">E321</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E7:62_1_9"/><b>then </b><i><font color="Green">E322</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/><a NAME="E8:62_1_9"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="finseq_5.html#T2">FINSEQ_5:2</a></i>;<br/><a NAME="E9:62_1_9"/><b>then </b><i><font color="Green">E323</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E10:62_1_9"/><i><font color="Green">E324</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E11:62_1_9"/><i><font color="Green">E325</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E12:62_1_9"/><i><font color="Green">E326</font></i>: 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i>, , </i>;<br/><i><font color="Green">E327</font></i>:  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
<b>by </b><i><a class="ref" href="polynom3.html#D3" target="_self">Def3</a>, <a class="ref" href="binarith.html#T53">BINARITH:53</a></i>
;<br/><a NAME="E14:62_1_9"/><i><font color="Green">E328</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/> <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span></span>)</span> = 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>

;<br/><a NAME="E16:62_1_9"/><b>then </b><i><font color="Green">E329</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T8">FINSEQ_1:8</a></i>;<br/><a NAME="E17:62_1_9"/><i><font color="Green">E330</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E18:62_1_9"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon">lj</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, , <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E20:62_1_9"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span>
 ;<br/><a NAME="E21:62_1_9"/><b>then </b><i><font color="Green">E332</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="polynom3.html#D3" target="_self">Def3</a>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><b>then </b><i><font color="Green">E333</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">lj</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, , <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<font color="Maroon">j</font>

;<br/><a NAME="E23:62_1_9"/><i><font color="Green">E334</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E24:62_1_9"/>
<font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="polynom3.html#D3" target="_self">Def3</a>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E25:62_1_9"/><b>then </b><i><font color="Green">E335</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">j</font> <a href="xcmplx_0.html#K6">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="real_2.html#T173">REAL_2:173</a></i>;<br/><a NAME="E26:62_1_9"/>
<font color="Maroon">lj</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , , , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E27:62_1_9"/><b>then </b><i><font color="Green">E336</font></i>: 
<font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">lj</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">lj</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">lj</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">lj</font></span>)</span>,2</span>)</span>
 <b>by </b><i/>;<br/><i><font color="Green">E337</font></i>:  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">lj</font></span>)</span>,2</span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">lj</font></span>)</span>,2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
<b>by </b><i>, </i>
;<br/><i><font color="Green">E338</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">lj</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">lj</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, , , <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">lj</font>

;<br/><i><font color="Green">E339</font></i>:  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">lj</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">lj</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">lj</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>
<b>by </b><i>, , <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/> <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">lj</font></span>)</span></span>)</span> = 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">lj</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom3.html#D4" target="_self">Def4</a>, , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">j</font>

;<br/><a NAME="E32:62_1_9"/><b>then </b><i><font color="Green">E340</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">lj</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T8">FINSEQ_1:8</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">j</font> = 
<font color="Maroon">j</font>
<b>by </b><i>, , <a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">j</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, , <a class="ref" href="card_3.html#D2">CARD_3:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_5.html#K4">Rev</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="wsierp_1.html#K3">.</a> <font color="Maroon">j</font>
<b>by </b><i>, , <a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>
;<br/></div><b>end;</b></div><a NAME="E55:62_1"/><b>then </b><i><font color="Green">E341</font></i>: 
 <a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_5.html#K4">Rev</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom3.html#T6" target="_self">Th6</a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/><i><font color="Green">E342</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font></span>)</span> = 
 <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">f2</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T30">POLYNOM1:30</a></i>
<br/>.= 
 <a href="wsierp_1.html#K7">Sum</a> <span class="p1">(<span class="default"><a href="polynom1.html#K5">Card</a> <font color="Maroon">g2</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T30">POLYNOM1:30</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_11"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:62_1_11"/><i><font color="Green">E343</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
 <b>and </b><br/><a NAME="E2:62_1_11"/><i><font color="Green">E344</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span>
 <b>and </b><br/><a NAME="E3:62_1_11"/><i><font color="Green">E345</font></i>: 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 ;<br/><b>consider </b><font color="Maroon">i1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E5:62_1_11"/><i><font color="Green">E346</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 <b>and </b><br/><a NAME="E6:62_1_11"/><i><font color="Green">E347</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
 <b>and </b><br/><a NAME="E7:62_1_11"/><i><font color="Green">E348</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g2</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j1</font>
 <b>and </b><br/><a NAME="E8:62_1_11"/><i><font color="Green">E349</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T32">POLYNOM1:32</a></i>;<br/><b>consider </b><font color="Maroon">i2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E10:62_1_11"/><i><font color="Green">E350</font></i>: 
<font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">g2</font>
 <b>and </b><br/><a NAME="E11:62_1_11"/><i><font color="Green">E351</font></i>: 
<font color="Maroon">j2</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span>
 <b>and </b><br/><a NAME="E12:62_1_11"/><i><font color="Green">E352</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K7">Sum</a> <span class="p2">(<span class="default"><a href="polynom1.html#K5">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g2</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">j2</font>
 <b>and </b><br/><a NAME="E13:62_1_11"/><i><font color="Green">E353</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T32">POLYNOM1:32</a></i>;<br/><a NAME="E14:62_1_11"/><i><font color="Green">E354</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E15:62_1_11"/><b>then </b><i><font color="Green">E355</font></i>: 
<font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span>
 <b>by </b><i/>;<br/><a NAME="E16:62_1_11"/><i><font color="Green">E356</font></i>: 
<font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E17:62_1_11"/><b>then </b><i><font color="Green">E357</font></i>: 
<font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom3.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span>,2</span>)</span>
 <b>by </b><i/>;<br/><a NAME="E18:62_1_11"/>
( <font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span></span>)</span> &amp; <font color="Maroon">j2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, , <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E19:62_1_11"/><b>then </b><i><font color="Green">E358</font></i>: 
( <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">i2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">j1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">j2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 )
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E20:62_1_11"/><i><font color="Green">E359</font></i>: 
<font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E21:62_1_11"/><b>then </b><i><font color="Green">E360</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E22:62_1_11"/><i><font color="Green">E361</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E23:62_1_11"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">i1</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E24:62_1_11"/><b>then </b><i><font color="Green">E362</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><i><font color="Green">E363</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="polynom3.html#D4" target="_self">Def4</a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><a NAME="E26:62_1_11"/><i><font color="Green">E364</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/> <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>
<b>by </b><i>, </i>
;<br/><b>then </b><i><font color="Green">E365</font></i>:  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="polynom3.html#T8" target="_self">Th8</a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>

;<br/><a NAME="E29:62_1_11"/><i><font color="Green">E366</font></i>: 
<font color="Maroon">i2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E30:62_1_11"/><b>then </b><i><font color="Green">E367</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><a NAME="E31:62_1_11"/>
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">i2</font>
 <b>by </b><i>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E32:62_1_11"/><b>then </b><i><font color="Green">E368</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><i><font color="Green">E369</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">i2</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font>
<b>by </b><i>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
;<br/><a NAME="E34:62_1_11"/><i><font color="Green">E370</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/> <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span>,2</span>)</span> = 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span>,2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span>
<b>by </b><i>, </i>
;<br/><b>then </b><i><font color="Green">E371</font></i>:  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span>

;<br/><i><font color="Green">E372</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, <a class="ref" href="polynom3.html#T9" target="_self">Th9</a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom3.html#T7" target="_self">Th7</a>, , <a class="ref" href="polynom3.html#T9" target="_self">Th9</a>, </i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j1</font></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="finseqop.html#K4">|-&gt;</a> <span class="p3"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K6" target="_self">Decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span>,2</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span> <a href="polynom3.html#K3" target="_self">^</a> <span class="p1"><a href="polynom3.html#K2" target="_self">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">j2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j2</font></span>)</span></span><a href="polynom3.html#K2" target="_self">*&gt;</a></span>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">j2</font> <a href="binarith.html#K3">-'</a> 1</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">i2</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">j2</font></span>)</span></span><a href="finseq_4.html#K3">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><a NAME="E39:62_1_11"/><b>then </b>
( <font color="Maroon">i1</font> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> <a href="binarith.html#K3">-'</a> 1 &amp; <font color="Maroon">j1</font> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">j2</font> <a href="binarith.html#K3">-'</a> 1 )
 <b>by </b><i>, , , , <a class="ref" href="group_7.html#T3">GROUP_7:3</a></i>;<br/><b>hence </b><a NAME="E40:62_1_11"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="polynom3.html#D3" target="_self">Def3</a>, , , <a class="ref" href="binarith.html#T49">BINARITH:49</a></i>;<br/></div><b>end;</b></div><a NAME="E58:62_1"/><b>then </b><i><font color="Green">E373</font></i>: 
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/><a NAME="E59:62_1"/><b>then </b>
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i>, , <a class="ref" href="finseq_4.html#T76">FINSEQ_4:76</a></i>;<br/><a NAME="E60:62_1"/><b>then </b>
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font>, <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 <b>by </b><i>, , <a class="ref" href="rfinseq.html#T39">RFINSEQ:39</a></i>;<br/><b>then consider </b><font color="Maroon">P</font> being   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span><b> such that </b><br/><a NAME="E62:62_1"/><i><font color="Green">E374</font></i>: 
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g2</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">P</font>
 <b>by </b><i><a class="ref" href="rfinseq.html#T17">RFINSEQ:17</a></i>;<br/><b>reconsider </b><font color="Maroon">P</font> = <font color="Maroon">P</font> as   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span> <b>by </b><i><a class="txt" href="polynom3.html#E19:62_1"><i><font color="Green">E69</font></i></a></i>;<br/><a NAME="E64:62_1"/>
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g1</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">P</font>
 <b>by </b><i><a class="txt" href="polynom3.html#E11:62_1"><i><font color="Green">E64</font></i></a>, <a class="txt" href="polynom3.html#E23:62_1"><i><font color="Green">E72</font></i></a>, , </i>;<br/><b>hence </b><a NAME="E65:62_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">q</font></span>)</span> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="polynom3.html#T3" target="_self">Th3</a>, <a class="txt" href="polynom3.html#E7:62_1"><i><font color="Green">E44</font></i></a>, , , <a class="ref" href="rlvect_2.html#T9">RLVECT_2:9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:62"/>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">q</font></span>)</span> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">p</font> <a href="polynom3.html#K14" target="_self">*'</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="polynom3.html#K14" target="_self">*'</a> <font color="Maroon">r</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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