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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">  for <font color="Olive" title="b1">p</font> being    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">F</font></span>)</span> holds   <a href="ring_4.html#K3" title="RING_4:func.3">NormPolynomial</a> <font color="Olive" title="b1">p</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Olive" title="b1">p</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">F</font></span>)</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">  <a href="ring_4.html#K3" title="RING_4:func.3">NormPolynomial</a> <font color="Maroon" title="c2">p</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Maroon" title="c2">p</font></span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c3">a</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c4">b</font> =  <a href="ring_4.html#K3" title="RING_4:func.3">NormPolynomial</a> <font color="Maroon" title="c2">p</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">F</font></span>)</span> ;<br/>
<a NAME="E2:62"/><span class="lab"><font color="Green" title="E33">A</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="polynom3.html#K12" title="POLYNOM3:func.12">*'</a> <span class="p1">(<span class="default"><a href="polynom3.html#K10" title="POLYNOM3:func.10">1_.</a> <font color="Maroon" title="c1">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom3.html#T35" onmouseover="rs('polynom3/T35')" onmouseout="rh()">POLYNOM3:35</a></span>;<br/>
<a NAME="E3:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">B</font></span>: 
<font color="Maroon" title="c2">p</font> <a href="ring_4.html#R1" title="RING_4:pred.1">divides</a>  <a href="ring_4.html#K3" title="RING_4:func.3">NormPolynomial</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ring_4.html#T1" target="_self" onmouseover="rs('ring_4/T1')" onmouseout="rh()">T2</a>, <a class="ref" href="ring_4.html#T26" target="_self" onmouseover="rs('ring_4/T26')" onmouseout="rh()">np2</a></span>;<br/>
<a NAME="E4:62"/>
 <a href="ring_4.html#K3" title="RING_4:func.3">NormPolynomial</a> <font color="Maroon" title="c2">p</font> <a href="ring_4.html#R1" title="RING_4:pred.1">divides</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E33">A</font></span></a>, <a class="ref" href="ring_4.html#T25" target="_self" onmouseover="rs('ring_4/T25')" onmouseout="rh()">np1</a>, <a class="ref" href="ring_4.html#T1" target="_self" onmouseover="rs('ring_4/T1')" onmouseout="rh()">T2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:62"/>
 <a href="ring_4.html#K3" title="RING_4:func.3">NormPolynomial</a> <font color="Maroon" title="c2">p</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E34">B</font></span></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/>


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