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<span class="kw">set </span><font color="Maroon" title="c4">g</font> =  <a href="polynom5.html#K10" title="POLYNOM5:func.10">Polynomial-Function</a> (<font color="Maroon" title="c1">L</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>);<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="42_1_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><a href="polynom5.html#K10" title="POLYNOM5:func.10">Polynomial-Function</a> (<font color="Maroon" title="c1">L</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K10" title="POLYNOM5:func.10">Polynomial-Function</a> (<font color="Maroon" title="c1">L</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="polynom5.html#K10" title="POLYNOM5:func.10">Polynomial-Function</a> (<font color="Maroon" title="c1">L</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K10" title="POLYNOM5:func.10">Polynomial-Function</a> (<font color="Maroon" title="c1">L</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="polynom5.html#K10" title="POLYNOM5:func.10">Polynomial-Function</a> (<font color="Maroon" title="c1">L</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span> = 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>,<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom5.html#D13" onmouseover="rs('polynom5/D13')" onmouseout="rh()">POLYNOM5:def 13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c2">p</font>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c3">q</font>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom4.html#T19" onmouseover="rs('polynom4/T19')" onmouseout="rh()">POLYNOM4:19</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">x</font>)</span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c3">q</font>,<span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c5">x</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz2.html#T25" target="_self" onmouseover="rs('hurwitz2/T25')" onmouseout="rh()">Th25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">x</font>)</span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">x</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz2.html#T25" target="_self" onmouseover="rs('hurwitz2/T25')" onmouseout="rh()">Th25</a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">x</font>)</span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c5">x</font>)</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T31" onmouseover="rs('rlvect_1/T31')" onmouseout="rh()">RLVECT_1:31</a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>,<font color="Maroon" title="c5">x</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom4.html#T19" onmouseover="rs('polynom4/T19')" onmouseout="rh()">POLYNOM4:19</a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K10" title="POLYNOM5:func.10">Polynomial-Function</a> (<font color="Maroon" title="c1">L</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom5.html#D13" onmouseover="rs('polynom5/D13')" onmouseout="rh()">POLYNOM5:def 13</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>
<a NAME="E2:42_1_1"/><span class="kw">then </span>
 <a href="polynom5.html#K10" title="POLYNOM5:func.10">Polynomial-Function</a> (<font color="Maroon" title="c1">L</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font></span>)</span>) is  <a href="hurwitz2.html#V2" title="HURWITZ2:attr.2">odd</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E3:42_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="polynom3.html#K7" title="POLYNOM3:func.7">+</a> <font color="Maroon" title="c3">q</font> is  <a href="hurwitz2.html#V4" title="HURWITZ2:attr.4">odd</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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