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<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">f</font> be    <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> <span class="p2">(<span class="default"><a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="finseq_2.html#K3">*</a> , <font color="Maroon">g</font> be    <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> <span class="p2">(<span class="default"><a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="finseq_2.html#K3">*</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:158"/><i><font color="Green">E41</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span>
 <b>and </b><br/><a NAME="E2:158"/><i><font color="Green">E42</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span>
 <b>and </b><br/><a NAME="E3:158"/><i><font color="Green">E43</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#K4">dom</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f</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"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>and </b><br/><a NAME="E4:158"/><i><font color="Green">E44</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#K4">dom</a> <font color="Maroon">g</font> holds <br/><font color="Maroon">g</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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Olive">k</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon">Ff</font> =  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">Fg</font> =  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font>;<br/>
<b>set </b><font color="Maroon">db</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:158_1_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">f</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">k</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:158_1_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">k</font> = <font color="Maroon">k</font> 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="polynom1.html#T21" target="_self">Th21</a></i>;<br/><b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</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="E6:158_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E7:158_1_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
 <b>and </b><br/><a NAME="E8:158_1_1"/>
<font color="Maroon">k</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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i</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">j</font>
 <b>and </b><br/><a NAME="E9:158_1_1"/><i><font color="Green">E69</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <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="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T21" target="_self">Th21</a>, <a class="txt" href="polynom1.html#E1"><i><font color="Green">Lemma32</font></i></a></i>;<br/><b>set </b><font color="Maroon">ddbi1</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>;<br/><a NAME="E10:158_1_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T19" target="_self">Th19</a>, <a class="ref" href="polynom1.html#T22" target="_self">Th22</a></i>;<br/><b>consider </b><font color="Maroon">b1</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b2</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E12:158_1_1"/><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E13:158_1_1"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T22" target="_self">Th22</a>, <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/><b>reconsider </b><font color="Maroon">b1'</font> = <font color="Maroon">b1</font>, <font color="Maroon">b2'</font> = <font color="Maroon">b2</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E15:158_1_1"/><i><font color="Green">E108</font></i>: 
( <font color="Maroon">b1'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">b2'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b2</font> )
 ;<br/><a NAME="E16:158_1_1"/><b>then </b><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E17:158_1_1"/><i><font color="Green">E110</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, , <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><i><font color="Green">E111</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <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#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T24" target="_self">Th24</a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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 href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>

;<br/><b>then consider </b><font color="Maroon">b11</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b12</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E20:158_1_1"/><i><font color="Green">E112</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E21:158_1_1"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">b1</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b11</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b12</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="ref" href="polynom1.html#T29" target="_self">Th29</a>, <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E22:158_1_1"/><i><font color="Green">E114</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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="E23:158_1_1"/><i><font color="Green">E115</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E24:158_1_1"/>
<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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</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"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><b>then </b><i><font color="Green">E116</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">b2</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="ref" href="polynom1.html#T24" target="_self">Th24</a>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a>, , <a class="txt" href="polynom1.html#E15:158_1_1"><i><font color="Green">E108</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b12</font>,<font color="Maroon">b2</font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><a NAME="E26:158_1_1"/>
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b11</font> <a href="polynom1.html#K9" target="_self">+</a> <span class="p1">(<span class="default"><font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a>, </i>;<br/><b>then consider </b><font color="Maroon">i'</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="E28:158_1_1"/><i><font color="Green">E117</font></i>: 
<font color="Maroon">i'</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span>
 <b>and </b><br/><a NAME="E29:158_1_1"/><i><font color="Green">E194</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<span class="p2">(<span class="default"><font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T15" target="_self">Th15</a></i>;<br/><b>set </b><font color="Maroon">b3</font> = <font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font>;<br/><b>consider </b><font color="Maroon">j'</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="E31:158_1_1"/><i><font color="Green">E195</font></i>: 
<font color="Maroon">j'</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E32:158_1_1"/><i><font color="Green">E196</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b12</font>,<font color="Maroon">b2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T15" target="_self">Th15</a></i>;<br/><b>set </b><font color="Maroon">ddbi'2</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>;<br/><a NAME="E33:158_1_1"/><i><font color="Green">E199</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</font> <a href="hidden.html#R1">=</a> <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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T20" target="_self">Th20</a>, <a class="txt" href="polynom1.html#E17:158_1_1"><i><font color="Green">E110</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">b11'</font> = <font color="Maroon">b11</font>, <font color="Maroon">b3'</font> = <font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E35:158_1_1"/><i><font color="Green">E201</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">b11'</font>,<font color="Maroon">b3'</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom1.html#E18:158_1_1"><i><font color="Green">E111</font></i></a></i>;<br/><a NAME="E36:158_1_1"/><b>then </b><i><font color="Green">E202</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b11</font>
 <b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E37:158_1_1"/><i><font color="Green">E204</font></i>: 
 <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E23:158_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><i><font color="Green">E205</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <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#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E22:158_1_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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 href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>

;<br/><a NAME="E39:158_1_1"/><b>then </b><i><font color="Green">E206</font></i>: 
<font color="Maroon">j'</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom1.html#E20:158_1_1"><i><font color="Green">E112</font></i></a>, <a class="txt" href="polynom1.html#E23:158_1_1"><i><font color="Green">E115</font></i></a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E40:158_1_1"/><b>then </b><i><font color="Green">E207</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="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T33" target="_self">Th33</a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E41:158_1_1"/><i><font color="Green">E208</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font></span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">b12</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</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="polynom1.html#E20:158_1_1"><i><font color="Green">E112</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><i><font color="Green">E211</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</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"><span class="p3">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</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">j'</font></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j'</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom1.html#E22:158_1_1"><i><font color="Green">E114</font></i></a>, <a class="ref" href="polynom1.html#T34" target="_self">Th34</a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">b11</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b12</font>,<font color="Maroon">b2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="txt" href="polynom1.html#E21:158_1_1"><i><font color="Green">E113</font></i></a>, <a class="txt" href="polynom1.html#E25:158_1_1"><i><font color="Green">E116</font></i></a>, <a class="txt" href="polynom1.html#E28:158_1_1"><i><font color="Green">E117</font></i></a>, <a class="ref" href="polynom1.html#T35" target="_self">Th35</a>, , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b12</font>,<font color="Maroon">b2</font></span><a href="finseq_1.html#K11">*&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">m</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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i'</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">j'</font>;<br/><a NAME="E43:158_1_1"/><i><font color="Green">E212</font></i>: 
<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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i'</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">j'</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font></span>)</span>
 <b>by </b><i>, <a class="txt" href="polynom1.html#E17:158_1_1"><i><font color="Green">E110</font></i></a>, <a class="ref" href="polynom1.html#T34" target="_self">Th34</a>, </i>;<br/><a NAME="E44:158_1_1"/>
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</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" target="_self">Card</a> <span class="p4">(<span class="default"><font color="Maroon">g</font> <a href="finseq_1.html#K17">|</a> <span class="p5">(<span class="default"><font color="Maroon">i'</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">j'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j'</font>
 <b>by </b><i>, <a class="txt" href="polynom1.html#E17:158_1_1"><i><font color="Green">E110</font></i></a>, <a class="ref" href="polynom1.html#T34" target="_self">Th34</a>, </i>;<br/><b>hence </b><a NAME="E45:158_1_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">g</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T21" target="_self">Th21</a>, , <a class="txt" href="polynom1.html#E16:158_1_1"><i><font color="Green">E109</font></i></a>, , <a class="ref" href="polynom1.html#T36" target="_self">Th36</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="E2:158_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">g</font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">k</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:158_1"/><i><font color="Green">E213</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font></span>)</span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/><b>reconsider </b><font color="Maroon">k</font> = <font color="Maroon">k</font> 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="polynom1.html#T21" target="_self">Th21</a></i>;<br/><b>consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</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="E7:158_1"/><i><font color="Green">E214</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E8:158_1"/><i><font color="Green">E215</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
 <b>and </b><br/><a NAME="E9:158_1"/>
<font color="Maroon">k</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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i</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">j</font>
 <b>and </b><br/><a NAME="E10:158_1"/><i><font color="Green">E216</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <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="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T21" target="_self">Th21</a>, <a class="txt" href="polynom1.html#E1"><i><font color="Green">Lemma32</font></i></a></i>;<br/><b>set </b><font color="Maroon">ddbi1</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>;<br/><a NAME="E11:158_1"/><i><font color="Green">E217</font></i>: 
<font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T20" target="_self">Th20</a>, <a class="ref" href="polynom1.html#T22" target="_self">Th22</a></i>;<br/><b>consider </b><font color="Maroon">b1</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b2</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E13:158_1"/><i><font color="Green">E219</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E14:158_1"/><i><font color="Green">E220</font></i>: 
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b2</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T22" target="_self">Th22</a>, <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/><b>reconsider </b><font color="Maroon">b1'</font> = <font color="Maroon">b1</font>, <font color="Maroon">b2'</font> = <font color="Maroon">b2</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E16:158_1"/><i><font color="Green">E222</font></i>: 
( <font color="Maroon">b1'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b1</font> &amp; <font color="Maroon">b2'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b2</font> )
 ;<br/><a NAME="E17:158_1"/><b>then </b><i><font color="Green">E223</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E18:158_1"/><i><font color="Green">E224</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, , <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><i><font color="Green">E225</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <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#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T24" target="_self">Th24</a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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 href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>

;<br/><b>then consider </b><font color="Maroon">b11</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b12</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E21:158_1"/><i><font color="Green">E226</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E22:158_1"/><i><font color="Green">E227</font></i>: 
<font color="Maroon">b2</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b11</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b12</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a>, <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/><a NAME="E23:158_1"/><i><font color="Green">E257</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E24:158_1"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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="E25:158_1"/><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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</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">j</font> <a href="hidden.html#R1">=</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"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><b>then </b><i><font color="Green">E258</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font> = 
<span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">b1</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="ref" href="polynom1.html#T24" target="_self">Th24</a>, <a class="ref" href="polynom1.html#T29" target="_self">Th29</a>, , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b11</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/><a NAME="E27:158_1"/>
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <span class="p1">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</font></span>)</span> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b12</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a>, </i>;<br/><b>then consider </b><font color="Maroon">i'</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="E29:158_1"/><i><font color="Green">E259</font></i>: 
<font color="Maroon">i'</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span>
 <b>and </b><br/><a NAME="E30:158_1"/><i><font color="Green">E260</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</font></span>)</span>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T15" target="_self">Th15</a></i>;<br/><b>set </b><font color="Maroon">b3</font> = <font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</font>;<br/><b>consider </b><font color="Maroon">j'</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="E32:158_1"/><i><font color="Green">E261</font></i>: 
<font color="Maroon">j'</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E33:158_1"/><i><font color="Green">E262</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</font></span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b11</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="polynom1.html#T15" target="_self">Th15</a></i>;<br/><b>set </b><font color="Maroon">ddbi'2</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>;<br/><a NAME="E34:158_1"/><i><font color="Green">E263</font></i>: 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T19" target="_self">Th19</a>, </i>;<br/><b>reconsider </b><font color="Maroon">b3'</font> = <font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</font>, <font color="Maroon">b12'</font> = <font color="Maroon">b12</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E36:158_1"/><i><font color="Green">E265</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">b3'</font>,<font color="Maroon">b12'</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i/>;<br/><a NAME="E37:158_1"/><b>then </b><i><font color="Green">E266</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">b12</font>
 <b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><a NAME="E38:158_1"/><i><font color="Green">E267</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</font>
 <b>by </b><i>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/><i><font color="Green">E268</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <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#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></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"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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 href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>

;<br/><a NAME="E40:158_1"/><i><font color="Green">E269</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="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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="E41:158_1"/><i><font color="Green">E270</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</font></span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><font color="Maroon">b1</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b11</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="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><i><font color="Green">E271</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</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"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j'</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"><a href="finseq_1.html#K3">len</a> <span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i'</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</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/>.= 
<span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b11</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">b12</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i>, , , <a class="ref" href="polynom1.html#T33" target="_self">Th33</a>, <a class="ref" href="polynom1.html#T34" target="_self">Th34</a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b11</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K11">*&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">m</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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i'</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">j'</font>;<br/><a NAME="E43:158_1"/><i><font color="Green">E272</font></i>: 
<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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><font color="Maroon">i'</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">j'</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, , , , , </i>;<br/><a NAME="E44:158_1"/>
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</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" target="_self">Card</a> <span class="p4">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <span class="p5">(<span class="default"><font color="Maroon">i'</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">j'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j'</font>
 <b>by </b><i>, , , , , </i>;<br/><b>hence </b><a NAME="E45:158_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">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#T21" target="_self">Th21</a>, , , <a class="ref" href="polynom1.html#T35" target="_self">Th35</a>, , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:158"/><b>then </b><i><font color="Green">E273</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">f</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">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<a NAME="E7:158"/><i><font color="Green">E274</font></i>: 
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">k2</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:158_2"/><i><font color="Green">E276</font></i>: 
<font color="Maroon">k1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span>
 <b>and </b><br/><a NAME="E2:158_2"/><i><font color="Green">E277</font></i>: 
<font color="Maroon">k2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span>
 <b>and </b><br/><a NAME="E3:158_2"/><i><font color="Green">E278</font></i>: 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k2</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="E5:158_2"/><i><font color="Green">E281</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E6:158_2"/><i><font color="Green">E282</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
 <b>and </b><br/><a NAME="E7:158_2"/><i><font color="Green">E283</font></i>: 
<font color="Maroon">k1</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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f</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="E8:158_2"/><i><font color="Green">E284</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</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">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="txt" href="polynom1.html#E1"><i><font color="Green">Lemma32</font></i></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="E10:158_2"/><i><font color="Green">E287</font></i>: 
<font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E11:158_2"/><i><font color="Green">E288</font></i>: 
<font color="Maroon">j2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span>
 <b>and </b><br/><a NAME="E12:158_2"/><i><font color="Green">E289</font></i>: 
<font color="Maroon">k2</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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">f</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="E13:158_2"/><i><font color="Green">E290</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</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">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k2</font>
 <b>by </b><i>, <a class="txt" href="polynom1.html#E1"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">ddbi11</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>;<br/>
<a NAME="E14:158_2"/><i><font color="Green">E292</font></i>: 
<font color="Maroon">f</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="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T19" target="_self">Th19</a>, <a class="ref" href="polynom1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E15:158_2"/><i><font color="Green">E293</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font>
 
<b>by </b><i>, <a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">b11</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b12</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E17:158_2"/><i><font color="Green">E294</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E18:158_2"/>
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b11</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b12</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">b11'</font> = <font color="Maroon">b11</font>, <font color="Maroon">b12'</font> = <font color="Maroon">b12</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E20:158_2"/><i><font color="Green">E295</font></i>: 
( <font color="Maroon">b11'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b11</font> &amp; <font color="Maroon">b12'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b12</font> )
 
;<br/>
<a NAME="E21:158_2"/><b>then </b><i><font color="Green">E296</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b11</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E22:158_2"/><i><font color="Green">E297</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">b12</font>
 
<b>by </b><i>, , <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<i><font color="Green">E298</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</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#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <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#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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 href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>

;<br/>
<b>then consider </b><font color="Maroon">b111</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b112</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E25:158_2"/><i><font color="Green">E301</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b111</font>,<font color="Maroon">b112</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E26:158_2"/><i><font color="Green">E302</font></i>: 
<font color="Maroon">b11</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b111</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b112</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E27:158_2"/><i><font color="Green">E303</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E28:158_2"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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="E29:158_2"/><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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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> <a href="hidden.html#R1">=</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"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>then </b><i><font color="Green">E304</font></i>: <span class="p1">(<span class="default"><font color="Maroon">f</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"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b111</font>,<font color="Maroon">b112</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">b12</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , , , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">b111</font>,<font color="Maroon">b112</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K11">*&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">ddbi21</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>;<br/>
<a NAME="E31:158_2"/><i><font color="Green">E306</font></i>: 
<font color="Maroon">f</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"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T19" target="_self">Th19</a>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a></i>;<br/>
<a NAME="E32:158_2"/><i><font color="Green">E307</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font>
 
<b>by </b><i>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">b21</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b22</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E34:158_2"/><i><font color="Green">E310</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b21</font>,<font color="Maroon">b22</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E35:158_2"/>
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b21</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b22</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a>, <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">b21'</font> = <font color="Maroon">b21</font>, <font color="Maroon">b22'</font> = <font color="Maroon">b22</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E37:158_2"/><i><font color="Green">E313</font></i>: 
( <font color="Maroon">b21'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b21</font> &amp; <font color="Maroon">b22'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b22</font> )
 
;<br/>
<a NAME="E38:158_2"/><b>then </b><i><font color="Green">E314</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b21</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T35" target="_self">Th35</a>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E39:158_2"/><i><font color="Green">E315</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">b22</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T35" target="_self">Th35</a>, , <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<i><font color="Green">E316</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</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#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <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#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T33" target="_self">Th33</a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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 href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span>

;<br/>
<b>then consider </b><font color="Maroon">b211</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b212</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E42:158_2"/><i><font color="Green">E319</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b211</font>,<font color="Maroon">b212</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E43:158_2"/><i><font color="Green">E320</font></i>: 
<font color="Maroon">b21</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b211</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b212</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E44:158_2"/><i><font color="Green">E321</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></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="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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="E45:158_2"/><i><font color="Green">E322</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E46:158_2"/>
<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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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> <a href="hidden.html#R1">=</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"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">f</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"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b211</font>,<font color="Maroon">b212</font></span><a href="finseq_1.html#K10">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">b22</font></span><a href="finseq_1.html#K9">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, <a class="ref" href="polynom1.html#T33" target="_self">Th33</a>, <a class="ref" href="polynom1.html#T36" target="_self">Th36</a>, , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">b211</font>,<font color="Maroon">b212</font>,<font color="Maroon">b22</font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/>
<a NAME="E48:158_2"/><b>then </b><i><font color="Green">E323</font></i>: 
( <font color="Maroon">b111</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b211</font> &amp; <font color="Maroon">b112</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b212</font> &amp; <font color="Maroon">b12</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b22</font> )
 
<b>by </b><i><a class="ref" href="polynom1.html#T24" target="_self">Th24</a>, <a class="ref" href="polynom1.html#T29" target="_self">Th29</a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a>, , <a class="ref" href="group_7.html#T3">GROUP_7:3</a></i>;<br/>
<a NAME="E49:158_2"/><b>then </b>
<font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font>
 
<b>by </b><i>, <a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a>, , , , <a class="ref" href="polynom1.html#T34" target="_self">Th34</a>, <a class="ref" href="polynom1.html#T35" target="_self">Th35</a>, , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E50:158_2"/>
<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , <a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , , , , , , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:158"/>
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="158_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">k1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">k2</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:158_3"/><i><font color="Green">E324</font></i>: 
<font color="Maroon">k1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font></span>)</span>
 <b>and </b><br/><a NAME="E2:158_3"/><i><font color="Green">E325</font></i>: 
<font color="Maroon">k2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font></span>)</span>
 <b>and </b><br/><a NAME="E3:158_3"/><i><font color="Green">E326</font></i>: 
<span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k2</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="E5:158_3"/><i><font color="Green">E327</font></i>: 
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E6:158_3"/><i><font color="Green">E328</font></i>: 
<font color="Maroon">j1</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font></span>)</span>
 <b>and </b><br/><a NAME="E7:158_3"/><i><font color="Green">E329</font></i>: 
<font color="Maroon">k1</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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g</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="E8:158_3"/><i><font color="Green">E330</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g</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">g</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T23" target="_self">Th23</a>, <a class="txt" href="polynom1.html#E1"><i><font color="Green">Lemma32</font></i></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="E10:158_3"/><i><font color="Green">E331</font></i>: 
<font color="Maroon">i2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font>
 <b>and </b><br/><a NAME="E11:158_3"/><i><font color="Green">E332</font></i>: 
<font color="Maroon">j2</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font></span>)</span>
 <b>and </b><br/><a NAME="E12:158_3"/><i><font color="Green">E333</font></i>: 
<font color="Maroon">k2</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" target="_self">Card</a> <span class="p3">(<span class="default"><font color="Maroon">g</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="E13:158_3"/><i><font color="Green">E334</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">g</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">g</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">k2</font>
 <b>by </b><i>, <a class="txt" href="polynom1.html#E1"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">ddbi11</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>;<br/>
<a NAME="E14:158_3"/><i><font color="Green">E335</font></i>: 
<font color="Maroon">g</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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T20" target="_self">Th20</a>, <a class="ref" href="polynom1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E15:158_3"/><i><font color="Green">E336</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i1</font>
 
<b>by </b><i>, <a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">b11</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b12</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E17:158_3"/><i><font color="Green">E337</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b12</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E18:158_3"/>
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b11</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b12</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">b11'</font> = <font color="Maroon">b11</font>, <font color="Maroon">b12'</font> = <font color="Maroon">b12</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E20:158_3"/><i><font color="Green">E338</font></i>: 
( <font color="Maroon">b11'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b11</font> &amp; <font color="Maroon">b12'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b12</font> )
 
;<br/>
<a NAME="E21:158_3"/><b>then </b><i><font color="Green">E339</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b11</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E22:158_3"/><i><font color="Green">E340</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">b12</font>
 
<b>by </b><i>, , <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<i><font color="Green">E341</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</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#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <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#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</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/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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 href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>

;<br/>
<b>then consider </b><font color="Maroon">b111</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b112</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E25:158_3"/><i><font color="Green">E342</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b111</font>,<font color="Maroon">b112</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E26:158_3"/><i><font color="Green">E343</font></i>: 
<font color="Maroon">b12</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b111</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b112</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E27:158_3"/><i><font color="Green">E344</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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="E28:158_3"/><i><font color="Green">E345</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j1</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E29:158_3"/>
<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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</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> <a href="hidden.html#R1">=</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"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i1</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>then </b><i><font color="Green">E346</font></i>: <span class="p1">(<span class="default"><font color="Maroon">g</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"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">b11</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b111</font>,<font color="Maroon">b112</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , , , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">b11</font>,<font color="Maroon">b111</font>,<font color="Maroon">b112</font></span><a href="finseq_1.html#K11">*&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">ddbi21</font> =  <a href="polynom1.html#K21" target="_self">decomp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span>;<br/>
<a NAME="E31:158_3"/><i><font color="Green">E347</font></i>: 
<font color="Maroon">g</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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span> <a href="polynom1.html#K4" target="_self">^^</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T20" target="_self">Th20</a>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a></i>;<br/>
<a NAME="E32:158_3"/><i><font color="Green">E348</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i2</font>
 
<b>by </b><i>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">b21</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b22</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E34:158_3"/><i><font color="Green">E349</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b21</font>,<font color="Maroon">b22</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E35:158_3"/>
<font color="Maroon">b</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b21</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b22</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a>, <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">b21'</font> = <font color="Maroon">b21</font>, <font color="Maroon">b22'</font> = <font color="Maroon">b22</font> as    <a href="polynom1.html#M1" target="_self">Element</a> of  <a href="polynom1.html#K14" target="_self">Bags</a> <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E37:158_3"/><i><font color="Green">E350</font></i>: 
( <font color="Maroon">b21'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b21</font> &amp; <font color="Maroon">b22'</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b22</font> )
 
;<br/>
<a NAME="E38:158_3"/><b>then </b><i><font color="Green">E351</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">b21</font>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E39:158_3"/><i><font color="Green">E352</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">b22</font>
 
<b>by </b><i>, , <a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<i><font color="Green">E353</font></i>:  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</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#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <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#K21" target="_self">decomp</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T34" target="_self">Th34</a>, <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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"><a href="finseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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 href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span>

;<br/>
<b>then consider </b><font color="Maroon">b211</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font>, <font color="Maroon">b212</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E42:158_3"/><i><font color="Green">E354</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b211</font>,<font color="Maroon">b212</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>and </b><br/><a NAME="E43:158_3"/><i><font color="Green">E355</font></i>: 
<font color="Maroon">b22</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b211</font> <a href="polynom1.html#K9" target="_self">+</a> <font color="Maroon">b212</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , <a class="ref" href="polynom1.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E44:158_3"/><i><font color="Green">E356</font></i>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">j2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">j2</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>
<a NAME="E45:158_3"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></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="polynom1.html#K21" target="_self">decomp</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</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="E46:158_3"/><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#K21" target="_self">decomp</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 2</span>)</span></span>)</span></span>)</span> <a href="finseq_2.html#K2">|-&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"><span class="p5">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</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> <a href="hidden.html#R1">=</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"><span class="p4">(<span class="default"><a href="polynom1.html#K21" target="_self">decomp</a> <font color="Maroon">b</font></span>)</span> <a href="polynom1.html#K3" target="_self">/.</a> <font color="Maroon">i2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1</span>)</span></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default"><font color="Maroon">g</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"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><font color="Maroon">b21</font></span><a href="finseq_1.html#K9">*&gt;</a></span> <a href="finseq_1.html#K7">^</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">b211</font>,<font color="Maroon">b212</font></span><a href="finseq_1.html#K10">*&gt;</a></span>
<b>by </b><i><a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, <a class="ref" href="polynom1.html#T34" target="_self">Th34</a>, <a class="ref" href="polynom1.html#T36" target="_self">Th36</a>, , , <a class="ref" href="matrlin.html#D2">MATRLIN:def 2</a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">b21</font>,<font color="Maroon">b211</font>,<font color="Maroon">b212</font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T60">FINSEQ_1:60</a></i>
;<br/>
<a NAME="E48:158_3"/><b>then </b><i><font color="Green">E357</font></i>: 
( <font color="Maroon">b111</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b211</font> &amp; <font color="Maroon">b112</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b212</font> &amp; <font color="Maroon">b11</font> <a href="pboole.html#R6">=</a> <font color="Maroon">b21</font> )
 
<b>by </b><i><a class="ref" href="polynom1.html#T24" target="_self">Th24</a>, <a class="ref" href="polynom1.html#T29" target="_self">Th29</a>, <a class="ref" href="polynom1.html#T32" target="_self">Th32</a>, <a class="ref" href="polynom1.html#T33" target="_self">Th33</a>, <a class="ref" href="group_7.html#T3">GROUP_7:3</a></i>;<br/>
<a NAME="E49:158_3"/><b>then </b>
<font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font>
 
<b>by </b><i>, <a class="ref" href="polynom1.html#T27" target="_self">Th27</a>, <a class="ref" href="polynom1.html#T30" target="_self">Th30</a>, , , , <a class="ref" href="polynom1.html#T35" target="_self">Th35</a>, , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E50:158_3"/>
<font color="Maroon">k1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T28" target="_self">Th28</a>, , <a class="ref" href="polynom1.html#T31" target="_self">Th31</a>, , , , , , , , <a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:158"/><b>then </b>
 <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font>, <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a> 
 
<b>by </b><i><a class="ref" href="polynom1.html#T21" target="_self">Th21</a>, <a class="ref" href="polynom1.html#T22" target="_self">Th22</a>, <a class="ref" href="rfinseq.html#T39">RFINSEQ:39</a></i>;<br/>
<b>hence </b><a NAME="E10:158"/>
 ex <font color="Olive">p</font> being  <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span> st  <a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K15">FlattenSeq</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Olive">p</font>
 <b>by </b><i><a class="ref" href="rfinseq.html#T17">RFINSEQ:17</a></i>;<br/>


</div>
