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<b>let </b><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="polyalg1.html#D1" target="_self" title="POLYALG1:def.1">POLYALG1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c2">L</font></span>)</span> holds  <font color="Maroon" title="c3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">y</font></span><br/><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c2">L</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span><br/>



<b>reconsider </b><font color="Maroon" title="c6">x1</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c7">y1</font> = <font color="Maroon" title="c5">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c2">L</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">p</font> = <font color="Maroon" title="c6">x1</font>, <font color="Maroon" title="c9">q</font> = <font color="Maroon" title="c7">y1</font> as   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c2">L</font> <b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>;<br/>
<a NAME="E3:28_1_1"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="polynom5.html#K3" title="POLYNOM5:func.3">*</a> <font color="Maroon" title="c8">p</font>
 
<b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>;<br/>
<a NAME="E4:28_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c9">q</font>
 
<b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font></span>)</span> = 
<font color="Maroon" title="c3">a</font> <a href="polynom5.html#K3" title="POLYNOM5:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">p</font> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c9">q</font></span>)</span>
<b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="polynom5.html#K3" title="POLYNOM5:func.3">*</a> <font color="Maroon" title="c8">p</font></span>)</span> <a href="polynom3.html#K11" title="POLYNOM3:func.11">*'</a> <font color="Maroon" title="c9">q</font>
<b>by </b><i><a class="ref" href="polyalg1.html#T10" target="_self" title="POLYALG1:th.10">Th10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c4">x</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c5">y</font>
<b>by </b><i><a class="txt" href="polyalg1.html#E3:28_1_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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