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<span class="kw">set </span><font color="Maroon" title="c4">Z</font> =  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c5">O</font> = <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>)</span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> (<span class="p1">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c3">a</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">O</font> = <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>)</span>)</span> <a href="funct_7.html#K15" title="FUNCT_7:func.15">+*</a> (<span class="p1">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c3">a</font>) as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">X</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/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">O9</font> = <font color="Maroon" title="c6">O</font> as   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of <span class="p1">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">X</font></span>)</span>,<font color="Maroon" title="c2">L</font> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">O9</font> = <font color="Maroon" title="c7">O9</font> as   <a href="polynom1.html#NM1" title="POLYNOM1:NM.1">Series</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">b</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c8">O9</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <font color="Maroon" title="c9">b</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/><a NAME="E1:39_1_1_1"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/> <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>)</span>)</span> = 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p2">(<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></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D7" title="POLYNOM1:def.7">POLYNOM1:def 7</a></span>
<br/>.= 
 <a href="pre_poly.html#K15" title="PRE_POLY:func.15">Bags</a> <font color="Maroon" title="c1">X</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>
;<br/><a NAME="E3:39_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<font color="Maroon" title="c8">O9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>)</span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#D3" title="FUNCT_7:def.3">FUNCT_7:def 3</a></span>;<br/><span class="kw">assume </span><a NAME="E4:39_1_1_1"/>
<font color="Maroon" title="c9">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">O9</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <font color="Maroon" title="c9">b</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/><a NAME="E5:39_1_1_1"/><span class="kw">then </span>
 not <font color="Maroon" title="c9">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K16" title="PRE_POLY:func.16">EmptyBag</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_1_1_1"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><font color="Maroon" title="c8">O9</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <font color="Maroon" title="c9">b</font> = 
<span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>)</span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <font color="Maroon" title="c9">b</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_1_1_1"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="funct_4.html#T11" title="FUNCT_4:th.11">FUNCT_4:11</a></span>
<br/>.= 
 <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="ref" href="polynom1.html#T22" title="POLYNOM1:th.22">POLYNOM1:22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:39_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> (<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font>) is  <a href="polynom7.html#V4" title="POLYNOM7:attr.4">Constant</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D7" target="_self" title="POLYNOM7:def.7">Def8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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