<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font> be   <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">L</font></span>)</span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">r</font></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">p1</font> = <font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c6">q1</font> = <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c7">r1</font> = <font color="Maroon" title="c4">r</font> as   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom3.html#D10" target="_self" onmouseover="rs('polynom3/D10')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E2:65_1_1"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">q1</font> <a href="normsp_1.html#K1" title="NORMSP_1:func.1">+</a> <font color="Maroon" title="c7">r1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom3.html#D10" target="_self" onmouseover="rs('polynom3/D10')" onmouseout="rh()">Def10</a></span>;<br/>
<a NAME="E3:65_1_1"/>
<font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> <a href="normsp_1.html#K1" title="NORMSP_1:func.1">+</a> <font color="Maroon" title="c6">q1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom3.html#D10" target="_self" onmouseover="rs('polynom3/D10')" onmouseout="rh()">Def10</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">r</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">p1</font> <a href="normsp_1.html#K1" title="NORMSP_1:func.1">+</a> <font color="Maroon" title="c6">q1</font></span>)</span> <a href="normsp_1.html#K1" title="NORMSP_1:func.1">+</a> <font color="Maroon" title="c7">r1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom3.html#D10" target="_self" onmouseover="rs('polynom3/D10')" onmouseout="rh()">Def10</a></span>
<br/>.= 
<font color="Maroon" title="c5">p1</font> <a href="normsp_1.html#K1" title="NORMSP_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">q1</font> <a href="normsp_1.html#K1" title="NORMSP_1:func.1">+</a> <font color="Maroon" title="c7">r1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom3.html#T26" target="_self" onmouseover="rs('polynom3/T26')" onmouseout="rh()">Th24</a></span>
<br/>.= 
<font color="Maroon" title="c2">p</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1_1"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="polynom3.html#D10" target="_self" onmouseover="rs('polynom3/D10')" onmouseout="rh()">Def10</a></span>
;<br/> <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>
