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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T</font> being  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>   <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font><br/> for <font color="Olive" title="b2">L</font> being non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</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> <br/> for <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">p2</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>  holds <br/>(  <a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">p2</font>,<font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font> or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">p2</font>,<font color="Olive" title="b1">T</font></span>)</span>,<font color="Olive" title="b1">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b1">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Olive" title="b4">p2</font>,<font color="Olive" title="b1">T</font></span>)</span>,<font color="Olive" title="b1">T</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">T</font> be   <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>   <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</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> <br/> for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>  holds <br/>(  <a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font> or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Olive" title="b2">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be  non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="algstr_0.html#V33" title="ALGSTR_0:attr.33">almost_left_invertible</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  <a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Olive" title="b1">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">p1</font>, <font color="Maroon" title="c5">p2</font> be   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:38"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
 <a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">sp</font> =  <a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">g1</font> = <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">g2</font> = <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:38_1"/>
( <font color="Maroon" title="c4">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or <font color="Maroon" title="c5">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or ( <font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_1"><span class="kw">suppose </span></a><a NAME="E1:38_1_1"/>
( <font color="Maroon" title="c4">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or <font color="Maroon" title="c5">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:38_1_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="groeb_2.html#T25" target="_self" title="GROEB_2:th.25">Th25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="38_1_2"><span class="kw">suppose </span></a><a NAME="E1:38_1_2"/><span class="lab"><font color="Green" title="E21">A2</font></span>: 
( <font color="Maroon" title="c4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c5">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><a NAME="E2:38_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A3</font></span>: 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>;<br/><a NAME="E3:38_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A4</font></span>: 
not  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D12" title="STRUCT_0:def.12">STRUCT_0:def 12</a></span>;<br/><span class="lab"><font color="Green" title="E24">A5</font></span>:  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:38_1_2"><span class="lab"><font color="Green" title="E23">A4</font></span></a>, <a class="ref" href="polynom7.html#T10" title="POLYNOM7:th.10">POLYNOM7:10</a></span>
;<br/><a NAME="E5:38_1_2"/><span class="lab"><font color="Green" title="E25">A6</font></span>: 
<font color="Maroon" title="c4">p1</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_2"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/> <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T9" title="POLYNOM7:th.9">POLYNOM7:9</a></span>
;<br/><a NAME="E7:38_1_2"/><span class="kw">then </span>
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:38_1_2"><span class="lab"><font color="Green" title="E22">A3</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>;<br/><a NAME="E8:38_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A7</font></span>: 
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/><span class="lab"><font color="Green" title="E27">A8</font></span>:  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span>,<font color="Maroon" title="c2">T</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T22" title="POLYRED:th.22">POLYRED:22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38_1_2"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E8:38_1_2"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="termord.html#T32" title="TERMORD:th.32">TERMORD:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T9" title="POLYNOM7:th.9">POLYNOM7:9</a></span>
;<br/><a NAME="E10:38_1_2"/><span class="lab"><font color="Green" title="E28">A9</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> <a href="pre_poly.html#R3" title="PRE_POLY:pred.3">divides</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_2.html#T7" target="_self" title="GROEB_2:th.7">Th7</a></span>;<br/><span class="lab"><font color="Green" title="E29">A10</font></span>:  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span>,<font color="Maroon" title="c2">T</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T22" title="POLYRED:th.22">POLYRED:22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:38_1_2"><span class="lab"><font color="Green" title="E25">A6</font></span></a>, <a class="txt" href="#E8:38_1_2"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="termord.html#T31" title="TERMORD:th.31">TERMORD:31</a></span>
<br/>.= 
 <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:38_1_2"><span class="lab"><font color="Green" title="E28">A9</font></span></a>, <a class="txt" href="#E4:38_1_2"><span class="lab"><font color="Green" title="E24">A5</font></span></a>, <a class="ref" href="groeb_2.html#D1" target="_self" title="GROEB_2:def.1">Def1</a></span>
;<br/><a NAME="E12:38_1_2"/><span class="lab"><font color="Green" title="E30">A11</font></span>: 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_2"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>;<br/><a NAME="E13:38_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A12</font></span>: 
not  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D12" title="STRUCT_0:def.12">STRUCT_0:def 12</a></span>;<br/><span class="lab"><font color="Green" title="E32">A13</font></span>:  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:38_1_2"><span class="lab"><font color="Green" title="E31">A12</font></span></a>, <a class="ref" href="polynom7.html#T10" title="POLYNOM7:th.10">POLYNOM7:10</a></span>
;<br/><a NAME="E15:38_1_2"/><span class="lab"><font color="Green" title="E33">A14</font></span>: 
<font color="Maroon" title="c5">p2</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38_1_2"><span class="lab"><font color="Green" title="E21">A2</font></span></a>, <a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/> <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T9" title="POLYNOM7:th.9">POLYNOM7:9</a></span>
;<br/><a NAME="E17:38_1_2"/><span class="kw">then </span>
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:38_1_2"><span class="lab"><font color="Green" title="E30">A11</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>;<br/><a NAME="E18:38_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A15</font></span>: 
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/><a NAME="E19:38_1_2"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:38"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E20:38_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A16</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E21:38_1_2"/><span class="lab"><font color="Green" title="E36">A17</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> <a href="pre_poly.html#R3" title="PRE_POLY:pred.3">divides</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_2.html#T7" target="_self" title="GROEB_2:th.7">Th7</a></span>;<br/><span class="lab"><font color="Green" title="E37">A18</font></span>:  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span>,<font color="Maroon" title="c2">T</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T22" title="POLYRED:th.22">POLYRED:22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:38_1_2"><span class="lab"><font color="Green" title="E33">A14</font></span></a>, <a class="txt" href="#E18:38_1_2"><span class="lab"><font color="Green" title="E34">A15</font></span></a>, <a class="ref" href="termord.html#T32" title="TERMORD:th.32">TERMORD:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T9" title="POLYNOM7:th.9">POLYNOM7:9</a></span>
;<br/><span class="lab"><font color="Green" title="E38">A19</font></span>:  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K11" title="POLYNOM1:func.11">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span>,<font color="Maroon" title="c2">T</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T22" title="POLYRED:th.22">POLYRED:22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:38_1_2"><span class="lab"><font color="Green" title="E33">A14</font></span></a>, <a class="txt" href="#E18:38_1_2"><span class="lab"><font color="Green" title="E34">A15</font></span></a>, <a class="ref" href="termord.html#T31" title="TERMORD:th.31">TERMORD:31</a></span>
<br/>.= 
 <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:38_1_2"><span class="lab"><font color="Green" title="E36">A17</font></span></a>, <a class="txt" href="#E14:38_1_2"><span class="lab"><font color="Green" title="E32">A13</font></span></a>, <a class="ref" href="groeb_2.html#D1" target="_self" title="GROEB_2:def.1">Def1</a></span>
;<br/><span class="kw">then </span><span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1:def 22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:38_1_2"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="txt" href="#E23:38_1_2"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:38_1_2"><span class="lab"><font color="Green" title="E27">A8</font></span></a>, <a class="txt" href="#E22:38_1_2"><span class="lab"><font color="Green" title="E37">A18</font></span></a>, <a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></span>
;<br/><a NAME="E25:38_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A20</font></span>: 
not  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><a NAME="E26:38_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K2" title="TERMORD:func.2">max</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="groeb_2.html#K1" title="GROEB_2:func.1">/</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_1.html#T7" title="GROEB_1:th.7">GROEB_1:7</a></span>;<br/><a NAME="E27:38_1_2"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:38_1_2"><span class="lab"><font color="Green" title="E29">A10</font></span></a>, <a class="txt" href="#E23:38_1_2"><span class="lab"><font color="Green" title="E38">A19</font></span></a>, <a class="ref" href="termord.html#T12" title="TERMORD:th.12">TERMORD:12</a></span>;<br/><span class="kw">hence </span><a NAME="E28:38_1_2"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_2.html#K3" title="GROEB_2:func.3">S-Poly</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="groeb_2.html#K2" title="GROEB_2:func.2">lcm</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:38_1_2"><span class="lab"><font color="Green" title="E35">A16</font></span></a>, <a class="txt" href="#E25:38_1_2"><span class="lab"><font color="Green" title="E39">A20</font></span></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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