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<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">T</font> be  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#V2">admissible</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V9">Field-like</a> non <a href="vectsp_1.html#V10">degenerated</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">f</font> be  <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Maroon">p</font> be  <a href="polynom7.html#V1">non-zero</a> <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>







<b>assume </b><a NAME="E1:13"/>
<font color="Maroon">f</font> <a href="polyred.html#R6">is_reducible_wrt</a> <font color="Maroon">p</font>,<font color="Maroon">T</font>
 ;<br/>

<b>then consider </b><font color="Maroon">b</font> being   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font><b> such that </b><br/><a NAME="E3:13"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">f</font> &amp;  <a href="termord.html#K3">HT</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="polynom1.html#R3">divides</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="polyred.html#T36">POLYRED:36</a></i>;<br/>
<a NAME="E4:13"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">b</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 
<b>by </b><i>, <a class="ref" href="termord.html#D6">TERMORD:def 6</a></i>;<br/>
<a NAME="E5:13"/>
 <a href="termord.html#K3">HT</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">b</font>,<font color="Maroon">T</font>
 
<b>by </b><i>, <a class="ref" href="termord.html#T10">TERMORD:10</a></i>;<br/>
<b>hence </b><a NAME="E6:13"/>
 <a href="termord.html#K3">HT</a> <font color="Maroon">p</font>,<font color="Maroon">T</font> <a href="termord.html#R1">&lt;=</a>  <a href="termord.html#K3">HT</a> <font color="Maroon">f</font>,<font color="Maroon">T</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="termord.html#T8">TERMORD:8</a></i>;<br/>


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