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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/> for <font color="Olive" title="b2">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font><br/> for <font color="Olive" title="b3">m</font> being  <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font><br/> for <font color="Olive" title="b4">b</font> being  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">m</font> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Olive" title="b2">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Olive" title="b3">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b4">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Olive" title="b3">m</font></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b4">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">L</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><br/> for <font color="Olive" title="b2">m</font> being  <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><br/> for <font color="Olive" title="b3">b</font> being  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Olive" title="b2">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Olive" title="b2">m</font></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b3">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">m</font> being  <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><br/> for <font color="Olive" title="b2">b</font> being  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Olive" title="b1">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Olive" title="b1">m</font></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b2">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">m</font> be   <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">b</font> being  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b1">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">b2</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c5">b2</font></span>)</span></span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">q</font> = <font color="Maroon" title="c4">m</font> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c3">p</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">b</font> = <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">s</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font><span class="kw"> such that </span><br/><a NAME="E2:18"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K7" title="RLVECT_1:func.7">Sum</a> <font color="Maroon" title="c8">s</font>
 <span class="kw">and </span><br/><a NAME="E3:18"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:18"/><span class="lab"><font color="Green" title="E18">A3</font></span>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">s</font> holds <br/> ex <font color="Olive" title="b2">b1</font>, <font color="Olive" title="b3">b2</font> being  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> st <br/>( <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">b2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> &amp; <font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b2">b1</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Olive" title="b3">b2</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D26" title="POLYNOM1:def.26">POLYNOM1:def 26</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E6:18"/><span class="lab"><font color="Green" title="E19">A4</font></span>: 
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:18"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c5">b2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T69" title="PRE_POLY:th.69">PRE_POLY:69</a></span>;<br/>
<span class="lab"><font color="Green" title="E21">A6</font></span>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">s</font> = 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">b19</font>, <font color="Maroon" title="c11">b29</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font><span class="kw"> such that </span><br/><a NAME="E10:18"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c10">b19</font>,<font color="Maroon" title="c11">b29</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E11:18"/><span class="lab"><font color="Green" title="E23">A8</font></span>: 
<font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c10">b19</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c11">b29</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A4</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E24">A9</font></span>: <font color="Maroon" title="c5">b2</font> = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span>,<font color="Maroon" title="c5">b2</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
<br/>.= 
<font color="Maroon" title="c11">b29</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
;<br/>
<a NAME="E13:18"/><span class="lab"><font color="Green" title="E25">A10</font></span>: 
for <font color="Olive" title="b1">k9</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">k9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">s</font> &amp; <font color="Olive" title="b1">k9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">k</font> holds <br/><font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c12">k9</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">s</font> &amp; <font color="Maroon" title="c12">k9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">k</font> implies <font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:18_3"/><span class="lab"><font color="Green" title="E26">A11</font></span>: 
<font color="Maroon" title="c12">k9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">s</font>
 <span class="kw">and </span><br/><a NAME="E2:18_3"/><span class="lab"><font color="Green" title="E27">A12</font></span>: 
<font color="Maroon" title="c12">k9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c13">b19</font>, <font color="Maroon" title="c14">b29</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font><span class="kw"> such that </span><br/><a NAME="E4:18_3"/><span class="lab"><font color="Green" title="E28">A13</font></span>: 
<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c13">b19</font>,<font color="Maroon" title="c14">b29</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E5:18_3"/><span class="lab"><font color="Green" title="E29">A14</font></span>: 
<font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c13">b19</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c14">b29</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="txt" href="#E1:18_3"><span class="lab"><font color="Green" title="E26">A11</font></span></a></span>;<br/>
<a NAME="E6:18_3"/><span class="lab"><font color="Green" title="E30">A15</font></span>: 
<font color="Maroon" title="c13">b19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K21" title="PRE_POLY:func.21">divisors</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E1:18_3"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E4:18_3"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="ref" href="pre_poly.html#T70" title="PRE_POLY:th.70">PRE_POLY:70</a></span>;<br/>
<span class="lab"><font color="Green" title="E31">A16</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Maroon" title="c13">b19</font> = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c13">b19</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</a> <font color="Maroon" title="c13">b19</font></span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c13">b19</font>,<font color="Maroon" title="c14">b29</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E1:18_3"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E4:18_3"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E6:18_3"><span class="lab"><font color="Green" title="E30">A15</font></span></a>, <a class="ref" href="pre_poly.html#D17" title="PRE_POLY:def.17">PRE_POLY:def 17</a></span>
<br/>.= 
<font color="Maroon" title="c14">b29</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_3_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_3_2"/>
( ( <font color="Maroon" title="c13">b19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font> &amp; <font color="Maroon" title="c14">b29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> ) or <font color="Maroon" title="c13">b19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font> or <font color="Maroon" title="c14">b29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_3_2_1"><span class="kw">suppose </span></a><a NAME="E1:18_3_2_1"/><span class="lab"><font color="Green" title="E32">A17</font></span>: 
( <font color="Maroon" title="c13">b19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font> &amp; <font color="Maroon" title="c14">b29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font></span><br/><div class="add"><span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">k9</font> = 
<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E1:18_3"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">decomp</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E4:18_3"><span class="lab"><font color="Green" title="E28">A13</font></span></a>, <a class="txt" href="#E1:18_3_2_1"><span class="lab"><font color="Green" title="E32">A17</font></span></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:18_3_2_1"/>
<font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="txt" href="#E1:18_3"><span class="lab"><font color="Green" title="E26">A11</font></span></a>, <a class="txt" href="#E2:18_3"><span class="lab"><font color="Green" title="E27">A12</font></span></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_3_2_2"><span class="kw">suppose </span></a><a NAME="E1:18_3_2_2"/>
<font color="Maroon" title="c13">b19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font></span><br/><div class="add"><a NAME="E2:18_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c13">b19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="polyred.html#E14"><span class="lab"><font color="Green" title="E14">Lm8</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:18_3_2_2"/>
<font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18_3"><span class="lab"><font color="Green" title="E29">A14</font></span></a>, <a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_3_2_3"><span class="kw">suppose </span></a><a NAME="E1:18_3_2_3"/>
<font color="Maroon" title="c14">b29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font></span><br/><div class="add"><a NAME="E2:18_3_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c13">b19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18_3"><span class="lab"><font color="Green" title="E31">A16</font></span></a>, <a class="ref" href="pre_poly.html#T48" title="PRE_POLY:th.48">PRE_POLY:48</a></span>;<br/><a NAME="E3:18_3_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c13">b19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="polyred.html#E14"><span class="lab"><font color="Green" title="E14">Lm8</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E4:18_3_2_3"/>
<font color="Maroon" title="c8">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">k9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18_3"><span class="lab"><font color="Green" title="E29">A14</font></span></a>, <a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font> = 
<span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c10">b19</font>,<font color="Maroon" title="c11">b29</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="txt" href="#E10:18"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
<br/>.= 
<font color="Maroon" title="c10">b19</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E15:18"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c5">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">m</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c4">m</font></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c5">b2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E8:18"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E6:18"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="txt" href="#E11:18"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="txt" href="#E12:18"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="txt" href="#E13:18"><span class="lab"><font color="Green" title="E25">A10</font></span></a>, <a class="ref" href="polynom2.html#T5" title="POLYNOM2:th.5">POLYNOM2:5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
