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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a> <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a> <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</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">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">z</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a>  <a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> 1,<font color="Olive" title="b1">z</font></span><br/><b>let </b><font color="Maroon" title="c2">z</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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">z</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a>  <a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> 1,<font color="Maroon" title="c2">z</font></span><br/>



 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> 1,<font color="Maroon" title="c2">z</font></span>)</span>,<font color="Maroon" title="c2">z</font> = 
<font color="Maroon" title="c2">z</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c2">z</font>
<b>by </b><i><a class="ref" href="hurwitz.html#T29" target="_self" title="HURWITZ:th.29">Th29</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28" title="RLVECT_1:th.28">RLVECT_1:28</a></i>
;<br/>
<b>hence </b><a NAME="E2:43"/>
<font color="Maroon" title="c2">z</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a>  <a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> 1,<font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="ref" href="polynom5.html#D6" title="POLYNOM5:def.6">POLYNOM5:def 6</a></i>; <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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