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<div class="add">

<span class="kw">set </span><font color="Maroon" title="c5">A</font> =  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">B</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">R1</font>, <font color="Maroon" title="c8">R2</font> be   <a href="relset_1.html#NM1" title="RELSET_1:NM.1">Relation</a> of <span class="p1">(<span class="default"><a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <span class="p2">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>; <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>, <font color="Olive" title="b2">q</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="c3">L</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R1</font> iff <font color="Olive" title="b1">p</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> ) ) &amp; ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</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="c3">L</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">R2</font> iff <font color="Olive" title="b1">p</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> ) ) implies <font color="Maroon" title="c7">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">R2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:76_1_2"/><span class="lab"><font color="Green" title="E58">A7</font></span>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</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="c3">L</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R1</font> iff <font color="Olive" title="b1">p</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font> )
 <span class="kw">and </span><br/><a NAME="E2:76_1_2"/><span class="lab"><font color="Green" title="E59">A8</font></span>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</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="c3">L</font> holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">R2</font> iff <font color="Olive" title="b1">p</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</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="c7">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">R2</font></span><br/>

<a NAME="E3:76_1_2"/>
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R1</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">R2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">p</font>, <font color="Maroon" title="c10">q</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R1</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">R2</font> )</span><br/>

<a NAME="E1:76_1_2_1"/><span class="lab"><font color="Green" title="E60">A9</font></span>: 
 <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E61">A10</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_2_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:76_1_2_1_1"/><span class="lab"><font color="Green" title="E62">A11</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">R2</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"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R1</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">p9</font>, <font color="Maroon" title="c12">q9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:76_1_2_1_1"/><span class="lab"><font color="Green" title="E63">A12</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">p9</font>,<font color="Maroon" title="c12">q9</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:76_1_2_1_1"/><span class="lab"><font color="Green" title="E64">A13</font></span>: 
<font color="Maroon" title="c11">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:76_1_2_1_1"/><span class="lab"><font color="Green" title="E65">A14</font></span>: 
<font color="Maroon" title="c12">q9</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 <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T6" title="RELSET_1:th.6">RELSET_1:6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">p9</font> = <font color="Maroon" title="c11">p9</font>, <font color="Maroon" title="c14">q9</font> = <font color="Maroon" title="c12">q9</font> as   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:76_1_2_1_1"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="txt" href="#E5:76_1_2_1_1"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></span>;<br/><a NAME="E7:76_1_2_1_1"/>
not <font color="Maroon" title="c13">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76_1_2_1"><span class="lab"><font color="Green" title="E60">A9</font></span></a>, <a class="txt" href="#E4:76_1_2_1_1"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E8:76_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">p9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">p9</font> = <font color="Maroon" title="c13">p9</font> as   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/><span class="lab"><font color="Green" title="E66">A15</font></span>: <font color="Maroon" title="c9">p</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p9</font>,<font color="Maroon" title="c14">q9</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76_1_2_1_1"><span class="lab"><font color="Green" title="E63">A12</font></span></a>, <a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c15">p9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
;<br/><span class="lab"><font color="Green" title="E67">A16</font></span>: <font color="Maroon" title="c10">q</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p9</font>,<font color="Maroon" title="c14">q9</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76_1_2_1_1"><span class="lab"><font color="Green" title="E63">A12</font></span></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c14">q9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></span>
;<br/><a NAME="E12:76_1_2_1_1"/>
<font color="Maroon" title="c15">p9</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Maroon" title="c14">q9</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76_1_2"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E1:76_1_2_1_1"><span class="lab"><font color="Green" title="E62">A11</font></span></a>, <a class="txt" href="#E3:76_1_2_1_1"><span class="lab"><font color="Green" title="E63">A12</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E13:76_1_2_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76_1_2"><span class="lab"><font color="Green" title="E58">A7</font></span></a>, <a class="txt" href="#E10:76_1_2_1_1"><span class="lab"><font color="Green" title="E66">A15</font></span></a>, <a class="txt" href="#E11:76_1_2_1_1"><span class="lab"><font color="Green" title="E67">A16</font></span></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="hs2(this)" href="javascript:()" title="76_1_2_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:76_1_2_1_2"/><span class="lab"><font color="Green" title="E62">A17</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R1</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"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">R2</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c11">p9</font>, <font color="Maroon" title="c12">q9</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:76_1_2_1_2"/><span class="lab"><font color="Green" title="E63">A18</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c11">p9</font>,<font color="Maroon" title="c12">q9</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">and </span><br/><a NAME="E4:76_1_2_1_2"/><span class="lab"><font color="Green" title="E64">A19</font></span>: 
<font color="Maroon" title="c11">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:76_1_2_1_2"/><span class="lab"><font color="Green" title="E65">A20</font></span>: 
<font color="Maroon" title="c12">q9</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 <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relset_1.html#T6" title="RELSET_1:th.6">RELSET_1:6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">p9</font> = <font color="Maroon" title="c11">p9</font>, <font color="Maroon" title="c14">q9</font> = <font color="Maroon" title="c12">q9</font> as   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:76_1_2_1_2"><span class="lab"><font color="Green" title="E64">A19</font></span></a>, <a class="txt" href="#E5:76_1_2_1_2"><span class="lab"><font color="Green" title="E65">A20</font></span></a>, <a class="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></span>;<br/><a NAME="E7:76_1_2_1_2"/>
not <font color="Maroon" title="c13">p9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76_1_2_1"><span class="lab"><font color="Green" title="E60">A9</font></span></a>, <a class="txt" href="#E4:76_1_2_1_2"><span class="lab"><font color="Green" title="E64">A19</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E8:76_1_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">p9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">p9</font> = <font color="Maroon" title="c13">p9</font> as   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/><span class="lab"><font color="Green" title="E66">A21</font></span>: <font color="Maroon" title="c9">p</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p9</font>,<font color="Maroon" title="c14">q9</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76_1_2_1_2"><span class="lab"><font color="Green" title="E63">A18</font></span></a>, <a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c15">p9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
;<br/><span class="lab"><font color="Green" title="E67">A22</font></span>: <font color="Maroon" title="c10">q</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">p9</font>,<font color="Maroon" title="c14">q9</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76_1_2_1_2"><span class="lab"><font color="Green" title="E63">A18</font></span></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c14">q9</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></span>
;<br/><a NAME="E12:76_1_2_1_2"/>
<font color="Maroon" title="c15">p9</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Maroon" title="c14">q9</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:76_1_2"><span class="lab"><font color="Green" title="E58">A7</font></span></a>, <a class="txt" href="#E1:76_1_2_1_2"><span class="lab"><font color="Green" title="E62">A17</font></span></a>, <a class="txt" href="#E3:76_1_2_1_2"><span class="lab"><font color="Green" title="E63">A18</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E13:76_1_2_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">R2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76_1_2"><span class="lab"><font color="Green" title="E59">A8</font></span></a>, <a class="txt" href="#E10:76_1_2_1_2"><span class="lab"><font color="Green" title="E66">A21</font></span></a>, <a class="txt" href="#E11:76_1_2_1_2"><span class="lab"><font color="Green" title="E67">A22</font></span></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>
<span class="kw">hence </span><a NAME="E4:76_1_2_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">R1</font> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">p</font>,<font color="Maroon" title="c10">q</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">R2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76_1_2_1"><span class="lab"><font color="Green" title="E61">A10</font></span></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>
<span class="kw">hence </span><a NAME="E4:76_1_2"/>
<font color="Maroon" title="c7">R1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">R2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D2" title="RELAT_1:def.2">RELAT_1:def 2</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>
