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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">x'</font> being  <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> st <br/>( <font color="Olive" title="b1">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; <font color="Olive" title="b1">x'</font> is <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a> );<br/>
<b>consider </b><font color="Maroon" title="c3">P</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p2">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font></span>)</span><b> such that </b><br/><a NAME="E2:184_1_1"/><i><font color="Green" title="E101">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">P</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] )
 <b>from </b><i><a class="ref" href="subset_1.html#S3" title="SUBSET_1:sch.3">SUBSET_1:sch 3</a>();<br/></i>
<b>consider </b><font color="Maroon" title="c4">x'</font> being  <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a> <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>;<br/>
<a NAME="E4:184_1_1"/>
<font color="Maroon" title="c4">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">P</font> = <font color="Maroon" title="c3">P</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p2">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font></span>)</span> <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $2 &amp; <font color="Olive" title="b3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $3 &amp; <font color="Olive" title="b1">p</font> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <font color="Olive" title="b2">q</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">r</font> );<br/>
<div><i><font color="Green" title="E102">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="184_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c5">P</font>;<br/><b>reconsider </b><font color="Maroon" title="c8">p</font> = <font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c9">q</font> = <font color="Maroon" title="c7">y</font> as    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> ;<br/><b>consider </b><font color="Maroon" title="c10">p'</font> being   <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><b> such that </b><br/><a NAME="E3:184_1_1_1"/><i><font color="Green" title="E103">A3</font></i>: 
( <font color="Maroon" title="c10">p'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">p</font> &amp; <font color="Maroon" title="c10">p'</font> is <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a> )
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c11">q'</font> being   <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><b> such that </b><br/><a NAME="E5:184_1_1_1"/><i><font color="Green" title="E104">A4</font></i>: 
( <font color="Maroon" title="c11">q'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">q</font> &amp; <font color="Maroon" title="c11">q'</font> is <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a> )
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c12">p'</font> = <font color="Maroon" title="c10">p'</font>, <font color="Maroon" title="c13">q'</font> = <font color="Maroon" title="c11">q'</font> as   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> <b>by </b><i><a class="txt" href="polynom1.html#E3:184_1_1_1"><i><font color="Green" title="E103">A3</font></i></a>, <a class="txt" href="polynom1.html#E5:184_1_1_1"><i><font color="Green" title="E104">A4</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c14">r</font> = <font color="Maroon" title="c12">p'</font> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <font color="Maroon" title="c13">q'</font>;<br/><a NAME="E7:184_1_1_1"/>
<font color="Maroon" title="c12">p'</font> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <font color="Maroon" title="c13">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c15">u</font> = <font color="Maroon" title="c12">p'</font> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <font color="Maroon" title="c13">q'</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c5">P</font> <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/><b>take </b><font color="Maroon" title="c16">u</font> = <font color="Maroon" title="c15">u</font>;<br/><b>thus </b><a NAME="E9:184_1_1_1"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c16">u</font>]
 <b>by </b><i><a class="txt" href="polynom1.html#E3:184_1_1_1"><i><font color="Green" title="E103">A3</font></i></a>, <a class="txt" href="polynom1.html#E5:184_1_1_1"><i><font color="Green" title="E104">A4</font></i></a></i>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c6">fadd</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c5">P</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c5">P</font><b> such that </b><br/><a NAME="E8:184_1_1"/><i><font color="Green" title="E103">A5</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c5">P</font> holds  <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c6">fadd</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S3" title="BINOP_1:sch.3">BINOP_1:sch 3</a>(<a class="txt" href="polynom1.html#E6:184_1_1"><i><font color="Green" title="E102">A2</font></i></a>);<br/></i>
<b>defpred </b><font color="Maroon">S<sub>3</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">r</font> being  <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $2 &amp; <font color="Olive" title="b3">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $3 &amp; <font color="Olive" title="b1">p</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Olive" title="b2">q</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">r</font> );<br/>
<div><i><font color="Green" title="E104">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="184_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c8">y</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c5">P</font>;<br/><b>reconsider </b><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c10">q</font> = <font color="Maroon" title="c8">y</font> as    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> ;<br/><b>consider </b><font color="Maroon" title="c11">p'</font> being   <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><b> such that </b><br/><a NAME="E3:184_1_1_2"/><i><font color="Green" title="E105">A7</font></i>: 
( <font color="Maroon" title="c11">p'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">p</font> &amp; <font color="Maroon" title="c11">p'</font> is <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a> )
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c12">q'</font> being   <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><b> such that </b><br/><a NAME="E5:184_1_1_2"/><i><font color="Green" title="E106">A8</font></i>: 
( <font color="Maroon" title="c12">q'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c10">q</font> &amp; <font color="Maroon" title="c12">q'</font> is <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a> )
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">p'</font> = <font color="Maroon" title="c11">p'</font>, <font color="Maroon" title="c14">q'</font> = <font color="Maroon" title="c12">q'</font> as   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> <b>by </b><i><a class="txt" href="polynom1.html#E3:184_1_1_2"><i><font color="Green" title="E105">A7</font></i></a>, <a class="txt" href="polynom1.html#E5:184_1_1_2"><i><font color="Green" title="E106">A8</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c15">r</font> = <font color="Maroon" title="c13">p'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c14">q'</font>;<br/><a NAME="E7:184_1_1_2"/>
<font color="Maroon" title="c13">p'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c14">q'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c16">u</font> = <font color="Maroon" title="c13">p'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c14">q'</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c5">P</font> <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/><b>take </b><font color="Maroon" title="c17">u</font> = <font color="Maroon" title="c16">u</font>;<br/><b>thus </b><a NAME="E9:184_1_1_2"/>
<font color="Maroon">S<sub>3</sub></font>[<font color="Maroon" title="c7">x</font>,<font color="Maroon" title="c8">y</font>,<font color="Maroon" title="c17">u</font>]
 <b>by </b><i><a class="txt" href="polynom1.html#E3:184_1_1_2"><i><font color="Green" title="E105">A7</font></i></a>, <a class="txt" href="polynom1.html#E5:184_1_1_2"><i><font color="Green" title="E106">A8</font></i></a></i>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c7">fmult</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c5">P</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c5">P</font><b> such that </b><br/><a NAME="E11:184_1_1"/><i><font color="Green" title="E105">A9</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c5">P</font> holds  <font color="Maroon">S<sub>3</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c7">fmult</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S3" title="BINOP_1:sch.3">BINOP_1:sch 3</a>(<a class="txt" href="polynom1.html#E9:184_1_1"><i><font color="Green" title="E104">A6</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c8">Z</font> = <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="rfunct_3.html#K5" title="RFUNCT_3:func.5">--&gt;</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> <b>by </b><i><a class="ref" href="funcop_1.html#T57" title="FUNCOP_1:th.57">FUNCOP_1:57</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">Z'</font> = <font color="Maroon" title="c8">Z</font> as   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">Z'</font> = <font color="Maroon" title="c9">Z'</font> as   <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c11">ZZ</font> = <font color="Maroon" title="c8">Z</font> as    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> <b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="184_1_1_3"><b>now </b></a><div class="add"><b>given </b><font color="Maroon" title="c12">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><a NAME="E2:184_1_1_3"/><i><font color="Green" title="E106">A10</font></i>: 
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">Z'</font>
 ;<br/><b>reconsider </b><font color="Maroon" title="c13">x</font> = <font color="Maroon" title="c12">x</font> as    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1_3"><i><font color="Green" title="E106">A10</font></i></a></i>;<br/><a NAME="E4:184_1_1_3"/>
<font color="Maroon" title="c10">Z'</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c13">x</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>
 <b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/><b>hence </b><a NAME="E5:184_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1_3"><i><font color="Green" title="E106">A10</font></i></a>, <a class="ref" href="polynom1.html#D9" target="_self" title="POLYNOM1:def.9">Def9</a></i>;<br/></div><b>end;</b></div>
<a NAME="E17:184_1_1"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c10">Z'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E18:184_1_1"/><b>then </b>
<font color="Maroon" title="c10">Z'</font> is <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a>
 
<b>by </b><i><a class="ref" href="polynom1.html#D10" target="_self" title="POLYNOM1:def.10">Def10</a></i>;<br/>
<a NAME="E19:184_1_1"/><b>then </b>
<font color="Maroon" title="c11">ZZ</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">P</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c12">Ze</font> = <font color="Maroon" title="c8">Z</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c5">P</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c13">O</font> = <font color="Maroon" title="c8">Z</font> <a href="polynom1.html#K1" title="POLYNOM1:func.1">+*</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">L</font></span>)</span> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c14">O'</font> = <font color="Maroon" title="c13">O</font> as   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c15">O'</font> = <font color="Maroon" title="c14">O'</font> as   <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c16">O</font> = <font color="Maroon" title="c13">O</font> as    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> <b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="184_1_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:184_1_1_4_1"/><i><font color="Green" title="E106">A11</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c15">O'</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c18">x'</font> = <font color="Maroon" title="c17">x</font> as    <a href="polynom1.html#M1" title="POLYNOM1:mode.1">Element</a> of  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font> ;<br/><b>assume </b><a NAME="E3:184_1_1_4_1"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 ;<br/><b>then </b><font color="Maroon" title="c15">O'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> = 
<font color="Maroon" title="c8">Z</font> <a href="polynom1.html#K15" title="POLYNOM1:func.15">.</a> <font color="Maroon" title="c18">x'</font>
<b>by </b><i><a class="ref" href="funct_7.html#T34" title="FUNCT_7:th.34">FUNCT_7:34</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
;<br/><b>hence </b><a NAME="E5:184_1_1_4_1"/>
contradiction
 <b>by </b><i><a class="txt" href="polynom1.html#E1:184_1_1_4_1"><i><font color="Green" title="E106">A11</font></i></a>, <a class="ref" href="polynom1.html#D9" target="_self" title="POLYNOM1:def.9">Def9</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:184_1_1_4"/><i><font color="Green" title="E106">A12</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font>
 ;<br/><a NAME="E3:184_1_1_4"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c8">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/><a NAME="E4:184_1_1_4"/><b>then </b>
<font color="Maroon" title="c15">O'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1_4"><i><font color="Green" title="E106">A12</font></i></a>, <a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>;<br/><a NAME="E5:184_1_1_4"/><b>then </b>
<font color="Maroon" title="c15">O'</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="ref" href="polynom1.html#T27" target="_self" title="POLYNOM1:th.27">Th27</a></i>;<br/><b>hence </b><a NAME="E6:184_1_1_4"/>
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c15">O'</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1_4"><i><font color="Green" title="E106">A12</font></i></a>, <a class="ref" href="polynom1.html#D9" target="_self" title="POLYNOM1:def.9">Def9</a></i>;<br/></div><b>end;</b></div>
<a NAME="E26:184_1_1"/><b>then </b>
 <a href="polynom1.html#K12" title="POLYNOM1:func.12">Support</a> <font color="Maroon" title="c15">O'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K16" title="POLYNOM1:func.16">EmptyBag</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E27:184_1_1"/><b>then </b>
<font color="Maroon" title="c15">O'</font> is <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a>
 
<b>by </b><i><a class="ref" href="polynom1.html#D10" target="_self" title="POLYNOM1:def.10">Def10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c17">O</font> = <font color="Maroon" title="c16">O</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c5">P</font> <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c18">R</font> =  <a href="vectsp_1.html#G3" title="VECTSP_1:aggr.3">doubleLoopStr</a>(# <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">fadd</font>,<font color="Maroon" title="c7">fmult</font>,<font color="Maroon" title="c17">O</font>,<font color="Maroon" title="c12">Ze</font> #) as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="vectsp_1.html#V3" title="VECTSP_1:attr.3">strict</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c18">R</font>
;<br/>

<b>thus </b><a NAME="E30:184_1_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c18">R</font> iff <font color="Olive" title="b1">x</font> is   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="184_1_1_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c19">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:184_1_1_5_1"/><i><font color="Green" title="E106">A13</font></i>: 
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c18">R</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c20">xx</font> = <font color="Maroon" title="c19">x</font> as    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> ;<br/><b>consider </b><font color="Maroon" title="c21">x'</font> being   <a href="polynom1.html#NM3" title="POLYNOM1:NM.3">Series</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><b> such that </b><br/><a NAME="E4:184_1_1_5_1"/><i><font color="Green" title="E107">A14</font></i>: 
( <font color="Maroon" title="c21">x'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c20">xx</font> &amp; <font color="Maroon" title="c21">x'</font> is <a href="polynom1.html#V2" title="POLYNOM1:attr.2">finite-Support</a> )
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a>, <a class="txt" href="polynom1.html#E1:184_1_1_5_1"><i><font color="Green" title="E106">A13</font></i></a></i>;<br/><b>thus </b><a NAME="E5:184_1_1_5_1"/>
<font color="Maroon" title="c19">x</font> is   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E4:184_1_1_5_1"><i><font color="Green" title="E107">A14</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:184_1_1_5"/><i><font color="Green" title="E106">A15</font></i>: 
<font color="Maroon" title="c19">x</font> is   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>
 ;<br/>

<a NAME="E3:184_1_1_5"/><b>then </b>
<font color="Maroon" title="c19">x</font> is    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <span class="p1">(<span class="default"><a href="polynom1.html#K14" title="POLYNOM1:func.14">Bags</a> <font color="Maroon" title="c1">n</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<b>hence </b><a NAME="E4:184_1_1_5"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c18">R</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E2:184_1_1"><i><font color="Green" title="E101">A1</font></i></a>, <a class="txt" href="polynom1.html#E2:184_1_1_5"><i><font color="Green" title="E106">A15</font></i></a></i>;<br/>


</div><b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c19">x</font>, <font color="Maroon" title="c20">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c18">R</font>;<br/><b>let </b><font color="Maroon" title="c21">p</font>, <font color="Maroon" title="c22">q</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>;<br/><b>assume </b><a NAME="E1:184_1_1_6"/><i><font color="Green" title="E106">A16</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">p</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">q</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c23">p'</font>, <font color="Maroon" title="c24">q'</font>, <font color="Maroon" title="c25">r'</font> being   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><b> such that </b><br/><a NAME="E3:184_1_1_6"/><i><font color="Green" title="E107">A17</font></i>: 
( <font color="Maroon" title="c23">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c24">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> &amp; <font color="Maroon" title="c25">r'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">fadd</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c19">x</font>,<font color="Maroon" title="c20">y</font> )
 <b>and </b><br/><a NAME="E4:184_1_1_6"/><i><font color="Green" title="E108">A18</font></i>: 
<font color="Maroon" title="c23">p'</font> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <font color="Maroon" title="c24">q'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c25">r'</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E8:184_1_1"><i><font color="Green" title="E103">A5</font></i></a></i>;<br/><b>thus </b><a NAME="E5:184_1_1_6"/>
<font color="Maroon" title="c19">x</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">p</font> <a href="polynom1.html#K22" title="POLYNOM1:func.22">+</a> <font color="Maroon" title="c22">q</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:184_1_1_6"><i><font color="Green" title="E106">A16</font></i></a>, <a class="txt" href="polynom1.html#E3:184_1_1_6"><i><font color="Green" title="E107">A17</font></i></a>, <a class="txt" href="polynom1.html#E4:184_1_1_6"><i><font color="Green" title="E108">A18</font></i></a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c19">x</font>, <font color="Maroon" title="c20">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c18">R</font>;<br/><b>let </b><font color="Maroon" title="c21">p</font>, <font color="Maroon" title="c22">q</font> be   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>;<br/><b>assume </b><a NAME="E1:184_1_1_7"/><i><font color="Green" title="E106">A19</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">p</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">q</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c23">p'</font>, <font color="Maroon" title="c24">q'</font>, <font color="Maroon" title="c25">r'</font> being   <a href="polynom1.html#NM4" title="POLYNOM1:NM.4">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font><b> such that </b><br/><a NAME="E3:184_1_1_7"/><i><font color="Green" title="E107">A20</font></i>: 
( <font color="Maroon" title="c23">p'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c24">q'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> &amp; <font color="Maroon" title="c25">r'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">fmult</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c19">x</font>,<font color="Maroon" title="c20">y</font> )
 <b>and </b><br/><a NAME="E4:184_1_1_7"/><i><font color="Green" title="E108">A21</font></i>: 
<font color="Maroon" title="c23">p'</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c24">q'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c25">r'</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E11:184_1_1"><i><font color="Green" title="E105">A9</font></i></a></i>;<br/><b>thus </b><a NAME="E5:184_1_1_7"/>
<font color="Maroon" title="c19">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">p</font> <a href="polynom1.html#K28" title="POLYNOM1:func.28">*'</a> <font color="Maroon" title="c22">q</font>
 <b>by </b><i><a class="txt" href="polynom1.html#E1:184_1_1_7"><i><font color="Green" title="E106">A19</font></i></a>, <a class="txt" href="polynom1.html#E3:184_1_1_7"><i><font color="Green" title="E107">A20</font></i></a>, <a class="txt" href="polynom1.html#E4:184_1_1_7"><i><font color="Green" title="E108">A21</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E33:184_1_1"/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c18">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K26" title="POLYNOM1:func.26">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>
 ;<br/>

<b>thus </b><a NAME="E34:184_1_1"/>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c18">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K27" title="POLYNOM1:func.27">1_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">L</font>
 ;<br/>


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