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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#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/> for <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">p2</font> being  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <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>  st  <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>, <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> <a href="groeb_2.html#R1" title="GROEB_2:pred.1">are_disjoint</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b1">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b4">p2</font>,<font color="Olive" title="b1">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Olive" title="b3">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Olive" title="b1">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b4">p2</font>,<font color="Olive" title="b1">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b1">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b1">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b4">p2</font>,<font color="Olive" title="b1">T</font></span>)</span></span>)</span>,<font color="Olive" title="b4">p2</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b1">T</font></span>)</span></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#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/> for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font> being  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <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>  st  <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>, <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> <a href="groeb_2.html#R1" title="GROEB_2:pred.1">are_disjoint</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b2">p1</font>,<font color="Maroon" title="c2">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c2">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Olive" title="b2">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b2">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b2">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b3">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>,<font color="Olive" title="b3">p2</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b2">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></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#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><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="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <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>  st  <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>, <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> <a href="groeb_2.html#R1" title="GROEB_2:pred.1">are_disjoint</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b1">p1</font>,<font color="Maroon" title="c2">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c2">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Olive" title="b1">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b1">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b2">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>,<font color="Olive" title="b2">p2</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Olive" title="b1">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p1</font>, <font color="Maroon" title="c5">p2</font> be   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <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="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="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="groeb_2.html#R1" title="GROEB_2:pred.1">are_disjoint</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  implies  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67"/><span class="lab"><font color="Green" title="E56">A1</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="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="groeb_2.html#R1" title="GROEB_2:pred.1">are_disjoint</a> 
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E57">A2</font></span>: 
(  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  &amp;  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">red1</font> =  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font>, <font color="Maroon" title="c7">red2</font> =  <a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font> as   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E57">A2</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">j</font> =  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ] <span class="kw">means </span>for <font color="Olive" title="b1">m</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Olive" title="b1">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Olive" title="b1">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Olive" title="b1">m</font></span>)</span></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:67_1"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><a NAME="E3:67_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">p2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:67_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</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>
<a NAME="E5:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A3</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></span>;<br/>
<a NAME="E6:67"/><span class="kw">then </span>
1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">j9</font> = <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></span>;<br/>
<span class="lab"><font color="Green" title="E59">A4</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,1</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T36" target="_self" title="GROEB_3:th.36">Th36</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><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>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T83" title="POLYNOM1:th.83">POLYNOM1:83</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><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>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T5" title="POLYRED:th.5">POLYRED:5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T4" title="POLYRED:th.4">POLYRED:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T36" target="_self" title="GROEB_3:th.36">Th36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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="polynom1.html#T85" title="POLYNOM1:th.85">POLYNOM1:85</a></span>
<br/>.= 
<font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#T38" title="TERMORD:th.38">TERMORD:38</a></span>
;<br/>
<a NAME="E9:67"/>
<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 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="E10:67"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font> <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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/>
<a NAME="E11:67"/><span class="kw">then </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="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font>
 
<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="E12:67"/><span class="kw">then </span>
for <font color="Olive" title="b1">t</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E13:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A5</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<span class="lab"><font color="Green" title="E61">A6</font></span>:  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font></span>)</span> = 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67"><span class="lab"><font color="Green" title="E60">A5</font></span></a>, <a class="ref" href="card_2.html#T63" title="CARD_2:th.63">CARD_2:63</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_2.html#T60" title="CARD_2:th.60">CARD_2:60</a></span>
;<br/>
<a NAME="E15:67"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A7</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">j9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T36" target="_self" title="GROEB_3:th.36">Th36</a></span>;<br/>
<a NAME="E16:67"/><span class="lab"><font color="Green" title="E63">A8</font></span>: 
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">j9</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">k</font> &amp; <font color="Maroon" title="c10">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">j9</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67_4"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">k</font>
 <span class="kw">and </span><br/><a NAME="E2:67_4"/><span class="lab"><font color="Green" title="E64">A9</font></span>: 
<font color="Maroon" title="c10">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">j9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font>] or <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1"/><span class="lab"><font color="Green" title="E65">A10</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:67_4_1_1"/>
(  <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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp;  <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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span>,<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#T31" title="TERMORD:th.31">TERMORD:31</a></span>;<br/><a NAME="E2:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A12</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</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="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#D7" title="TERMORD:def.7">TERMORD:def 7</a></span>;<br/><a NAME="E3:67_4_1_1"/><span class="lab"><font color="Green" title="E67">A13</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T35" title="TERMORD:th.35">TERMORD:35</a></span>;<br/><a NAME="E4:67_4_1_1"/>
<font color="Maroon" title="c7">red2</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 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="E5:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A15</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font> <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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><span class="kw">let </span><font color="Maroon" title="c11">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c11">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 implies  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E6:67_4_1_1"/><span class="lab"><font color="Green" title="E69">A16</font></span>: 
<font color="Maroon" title="c11">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E7:67_4_1_1"/><span class="lab"><font color="Green" title="E70">A17</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span><br/><span class="kw">set </span><font color="Maroon" title="c12">m9</font> = <font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1_1_1"/>
<font color="Maroon" title="c11">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:67_4_1_1_1"/><span class="kw">then </span>
 <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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="ref" href="groeb_3.html#T35" target="_self" title="GROEB_3:th.35">Th35</a></span>;<br/><span class="kw">hence </span><a NAME="E3:67_4_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67_4_1_1"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</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><a NAME="E9:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A18</font></span>: 
<font color="Maroon" title="c11">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E10:67_4_1_1"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T41" target="_self" title="GROEB_3:th.41">Th41</a>, <a class="ref" href="card_2.html#T63" title="CARD_2:th.63">CARD_2:63</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A19</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67_4_1_1"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E9:67_4_1_1"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="ref" href="groeb_3.html#T42" target="_self" title="GROEB_3:th.42">Th42</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T50" title="CARD_1:th.50">CARD_1:50</a></span>
;<br/><span class="kw">set </span><font color="Maroon" title="c13">f</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>;<br/><a NAME="E12:67_4_1_1"/><span class="lab"><font color="Green" title="E73">A20</font></span>: 
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D12" title="PRE_POLY:def.12">PRE_POLY:def 12</a></span>;<br/><a NAME="E13:67_4_1_1"/><span class="lab"><font color="Green" title="E74">A21</font></span>: 
<font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67_4_1_1"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:67_4_1_1_3"/><span class="lab"><font color="Green" title="E75">A22</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">red1</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">t</font></span>)</span> where <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">red1</font> &amp; <font color="Olive" title="b2">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T30" title="TERMORD:th.30">TERMORD:30</a></span>;<br/><span class="kw">assume </span><a NAME="E2:67_4_1_1_3"/>
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</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"><font color="Maroon" title="c6">red1</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:67_4_1_1_3"/><span class="kw">then </span>
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">t</font></span>)</span> where <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">red1</font> &amp; <font color="Olive" title="b2">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67_4_1_1_3"><span class="lab"><font color="Green" title="E75">A22</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">s</font>, <font color="Maroon" title="c15">t</font> being    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font><span class="kw"> such that </span><br/><a NAME="E5:67_4_1_1_3"/><span class="lab"><font color="Green" title="E76">A23</font></span>: 
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">s</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c15">t</font>
 <span class="kw">and </span><br/><a NAME="E6:67_4_1_1_3"/><span class="lab"><font color="Green" title="E77">A24</font></span>: 
<font color="Maroon" title="c14">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">red1</font>
 <span class="kw">and </span><br/><a NAME="E7:67_4_1_1_3"/><span class="lab"><font color="Green" title="E78">A25</font></span>: 
<font color="Maroon" title="c15">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ;<br/><a NAME="E8:67_4_1_1_3"/><span class="lab"><font color="Green" title="E79">A26</font></span>: 
<font color="Maroon" title="c15">t</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <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>,<font color="Maroon" title="c2">T</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_3_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_3_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_3_1_1_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="E1:67_4_1_1_3_1_1_1"/>
( <font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> or <font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_3_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:67_4_1_1_3_1_1_1_1"/>
<font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:67_4_1_1_3_1_1_1_1"/><span class="kw">then </span>
 <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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="ref" href="groeb_3.html#T35" target="_self" title="GROEB_3:th.35">Th35</a></span>;<br/><span class="kw">hence </span><a NAME="E3:67_4_1_1_3_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67_4_1_1_3"><span class="lab"><font color="Green" title="E78">A25</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</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="67_4_1_1_3_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:67_4_1_1_3_1_1_1_2"/><span class="lab"><font color="Green" title="E80">A27</font></span>: 
<font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c15">t</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <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>,<font color="Maroon" title="c2">T</font></span><br/><div class="add"><a NAME="E2:67_4_1_1_3_1_1_1_2"/><span class="lab"><font color="Green" title="E81">A28</font></span>: 
<font color="Maroon" title="c15">t</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="txt" href="#E7:67_4_1_1_3"><span class="lab"><font color="Green" title="E78">A25</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E3:67_4_1_1_3_1_1_1_2"/>
<font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E1:67_4_1_1_3_1_1_1_2"><span class="lab"><font color="Green" title="E80">A27</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><span class="kw">hence </span><a NAME="E4:67_4_1_1_3_1_1_1_2"/>
<font color="Maroon" title="c15">t</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <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>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67_4_1_1_3_1_1_1_2"><span class="lab"><font color="Green" title="E81">A28</font></span></a>, <a class="ref" href="groeb_3.html#T3" target="_self" title="GROEB_3:th.3">Th3</a>, <a class="ref" href="groeb_3.html#T39" target="_self" title="GROEB_3:th.39">Th39</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></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:67_4_1_1_3_1"/>
<font color="Maroon" title="c15">t</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <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>,<font color="Maroon" title="c2">T</font>
 ; <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><a NAME="E9:67_4_1_1_3"/>
<font color="Maroon" title="c14">s</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1_3"><span class="lab"><font color="Green" title="E77">A24</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E10:67_4_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c14">s</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c15">t</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</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> <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="c6">red1</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="#E8:67_4_1_1_3"><span class="lab"><font color="Green" title="E79">A26</font></span></a>, <a class="ref" href="groeb_3.html#T5" target="_self" title="GROEB_3:th.5">Th5</a></span>;<br/><a NAME="E11:67_4_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c14">s</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c15">t</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</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="ref" href="termord.html#T26" title="TERMORD:th.26">TERMORD:26</a></span>;<br/><span class="kw">hence </span><a NAME="E12:67_4_1_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67_4_1_1_3"><span class="lab"><font color="Green" title="E76">A23</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><a NAME="E15:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A29</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">red1</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="#E12:67_4_1_1"><span class="lab"><font color="Green" title="E73">A20</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><a NAME="E16:67_4_1_1"/><span class="lab"><font color="Green" title="E76">A30</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_4"><span class="kw">now </span></a><div class="add"><a NAME="E1:67_4_1_1_4"/>
<font color="Maroon" title="c6">red1</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 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="E2:67_4_1_1_4"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">red1</font> <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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E3:67_4_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A31</font></span>: 
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <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#R1" title="HIDDEN:pred.1">=</a>  <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> &amp;  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<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> <font color="Maroon" title="c6">red1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T26" title="TERMORD:th.26">TERMORD:26</a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E4:67_4_1_1_4"/><span class="lab"><font color="Green" title="E78">A32</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">t</font></span>)</span> where <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">s</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Olive" title="b2">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"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T30" title="TERMORD:th.30">TERMORD:30</a></span>;<br/><span class="kw">assume </span><a NAME="E5:67_4_1_1_4"/>
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</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"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E6:67_4_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A33</font></span>: 
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">s</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">t</font></span>)</span> where <font color="Olive" title="b1">s</font>, <font color="Olive" title="b2">t</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">s</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Olive" title="b2">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"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67_4_1_1_4"><span class="lab"><font color="Green" title="E78">A32</font></span></a></span>;<br/><a NAME="E7:67_4_1_1_4"/>
( <font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> &amp;  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_1.html#T5" title="GROEB_1:th.5">GROEB_1:5</a>, <a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>;<br/><a NAME="E8:67_4_1_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A34</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T79" title="POLYNOM1:th.79">POLYNOM1:79</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c14">s</font>, <font color="Maroon" title="c15">t</font> being    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font><span class="kw"> such that </span><br/><a NAME="E10:67_4_1_1_4"/><span class="lab"><font color="Green" title="E81">A35</font></span>: 
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">s</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c15">t</font>
 <span class="kw">and </span><br/><a NAME="E11:67_4_1_1_4"/><span class="lab"><font color="Green" title="E82">A36</font></span>: 
<font color="Maroon" title="c14">s</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E12:67_4_1_1_4"/><span class="lab"><font color="Green" title="E83">A37</font></span>: 
<font color="Maroon" title="c15">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"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1_4"><span class="lab"><font color="Green" title="E79">A33</font></span></a></span>;<br/><a NAME="E13:67_4_1_1_4"/><span class="lab"><font color="Green" title="E84">A38</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E16:67_4_1_1"><span class="lab"><font color="Green" title="E76">A30</font></span></a>, <a class="ref" href="groeb_3.html#T27" target="_self" title="GROEB_3:th.27">Th27</a></span>;<br/><a NAME="E14:67_4_1_1_4"/><span class="lab"><font color="Green" title="E85">A39</font></span>: 
<font color="Maroon" title="c15">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_4_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_4_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_4_1_1_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="E1:67_4_1_1_4_1_1_1"/>
( <font color="Maroon" title="c15">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font> or <font color="Maroon" title="c15">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:67_4_1_1_4"><span class="lab"><font color="Green" title="E83">A37</font></span></a>, <a class="txt" href="#E8:67_4_1_1_4"><span class="lab"><font color="Green" title="E80">A34</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_4_1_1_4_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:67_4_1_1_4_1_1_1_1"/>
<font color="Maroon" title="c15">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c15">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:67_4_1_1_4_1_1_1_1"/>
<font color="Maroon" title="c15">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 ; <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="67_4_1_1_4_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:67_4_1_1_4_1_1_1_2"/>
<font color="Maroon" title="c15">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c15">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:67_4_1_1_4_1_1_1_2"/>
<font color="Maroon" title="c15">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1_4"><span class="lab"><font color="Green" title="E84">A38</font></span></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></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:67_4_1_1_4_1"/>
<font color="Maroon" title="c15">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 ; <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><a NAME="E15:67_4_1_1_4"/>
 <a href="termord.html#K5" title="TERMORD:func.5">HM</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="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="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/><a NAME="E16:67_4_1_1_4"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E17:67_4_1_1_4"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T21" title="TERMORD:th.21">TERMORD:21</a></span>;<br/><a NAME="E18:67_4_1_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E11:67_4_1_1_4"><span class="lab"><font color="Green" title="E82">A36</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E19:67_4_1_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E10:67_4_1_1_4"><span class="lab"><font color="Green" title="E81">A35</font></span></a>, <a class="txt" href="#E3:67_4_1_1_4"><span class="lab"><font color="Green" title="E77">A31</font></span></a>, <a class="txt" href="#E14:67_4_1_1_4"><span class="lab"><font color="Green" title="E85">A39</font></span></a>, <a class="ref" href="groeb_3.html#T52" target="_self" title="GROEB_3:th.52">Th52</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><a NAME="E18:67_4_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="#E12:67_4_1_1"><span class="lab"><font color="Green" title="E73">A20</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><a NAME="E19:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A40</font></span>: 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="rlvect_1.html#T25" title="RLVECT_1:th.25">RLVECT_1:25</a></span>;<br/><a NAME="E20:67_4_1_1"/><span class="lab"><font color="Green" title="E78">A41</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_5"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1_1_5"/><span class="lab"><font color="Green" title="E79">A42</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">red2</font>,<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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div><span class="lab"><font color="Green" title="E80">A43</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_5_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c14">t</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c14">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font> implies <font color="Maroon" title="c14">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:67_4_1_1_5_1"/><span class="lab"><font color="Green" title="E81">A44</font></span>: 
<font color="Maroon" title="c14">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c14">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">t9</font> = <font color="Maroon" title="c14">t</font> as   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D12" title="PRE_POLY:def.12">PRE_POLY:def 12</a></span>;<br/><a NAME="E3:67_4_1_1_5_1"/>
(  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font> &amp; <font color="Maroon" title="c15">t9</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">red2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67_4_1_1_5_1"><span class="lab"><font color="Green" title="E81">A44</font></span></a>, <a class="ref" href="termord.html#T35" title="TERMORD:th.35">TERMORD:35</a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><span class="kw">hence </span><a NAME="E4:67_4_1_1_5_1"/>
<font color="Maroon" title="c14">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E20:67_4_1_1"><span class="lab"><font color="Green" title="E78">A41</font></span></a>, <a class="txt" href="#E1:67_4_1_1_5"><span class="lab"><font color="Green" title="E79">A42</font></span></a>, <a class="txt" href="#E1:67_4_1_1_5_1"><span class="lab"><font color="Green" title="E81">A44</font></span></a>, <a class="ref" href="groeb_3.html#T24" target="_self" title="GROEB_3:th.24">Th24</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><a NAME="E3:67_4_1_1_5"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E16:67_4_1_1"><span class="lab"><font color="Green" title="E76">A30</font></span></a>, <a class="ref" href="groeb_3.html#T27" target="_self" title="GROEB_3:th.27">Th27</a></span>;<br/><a NAME="E4:67_4_1_1_5"/><span class="kw">then </span>
for <font color="Olive" title="b1">t</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> holds <br/><font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 ;<br/><span class="kw">hence </span><a NAME="E5:67_4_1_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:67"><span class="lab"><font color="Green" title="E61">A6</font></span></a>, <a class="txt" href="#E2:67_4"><span class="lab"><font color="Green" title="E64">A9</font></span></a>, <a class="txt" href="#E11:67_4_1_1"><span class="lab"><font color="Green" title="E72">A19</font></span></a>, <a class="txt" href="#E2:67_4_1_1_5"><span class="lab"><font color="Green" title="E80">A43</font></span></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</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><a NAME="E22:67_4_1_1"/><span class="kw">then </span>
 <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">red2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67_4_1_1"><span class="lab"><font color="Green" title="E68">A15</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E23:67_4_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="ref" href="groeb_3.html#T12" target="_self" title="GROEB_3:th.12">Th12</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">z1</font> = <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> as   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <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> <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="kw">reconsider </span><font color="Maroon" title="c15">z</font> = <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c14">z1</font> as   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <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> ;<br/><a NAME="E26:67_4_1_1"/>
<font color="Maroon" title="c14">z1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></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/><a NAME="E27:67_4_1_1"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T79" title="POLYNOM1:th.79">POLYNOM1:79</a></span>;<br/><a NAME="E28:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A45</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_1.html#T5" title="GROEB_1:th.5">GROEB_1:5</a></span>;<br/><a NAME="E29:67_4_1_1"/>
<font color="Maroon" title="c15">z</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 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="E30:67_4_1_1"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c15">z</font> <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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">w</font> = <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c15">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T18" title="INT_1:th.18">INT_1:18</a>, <a class="ref" href="nat_1.html#T14" title="NAT_1:th.14">NAT_1:14</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c17">lowzw</font> =  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c15">z</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c16">w</font> as   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T37" target="_self" title="GROEB_3:th.37">Th37</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c18">b</font> =  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font>;<br/><span class="kw">set </span><font color="Maroon" title="c19">s</font> = <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>;<br/><a NAME="E33:67_4_1_1"/><span class="lab"><font color="Green" title="E80">A46</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c14">z1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">t9</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">t</font></span>)</span> where <font color="Olive" title="b1">t9</font>, <font color="Olive" title="b2">t</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">t9</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Olive" title="b2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T30" title="TERMORD:th.30">TERMORD:30</a></span>;<br/><a NAME="E34:67_4_1_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c15">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">w</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ;<br/><a NAME="E35:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A47</font></span>: 
<font color="Maroon" title="c16">w</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c15">z</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T16" title="NAT_1:th.16">NAT_1:16</a></span>;<br/><a NAME="E36:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A48</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c17">lowzw</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c15">z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T26" target="_self" title="GROEB_3:th.26">Th26</a></span>;<br/><a NAME="E37:67_4_1_1"/>
<font color="Maroon" title="c17">lowzw</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 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="E38:67_4_1_1"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c17">lowzw</font> <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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E39:67_4_1_1"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c17">lowzw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T7" title="POLYNOM7:th.7">POLYNOM7:7</a></span>;<br/><a NAME="E40:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A49</font></span>: 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c17">lowzw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E41:67_4_1_1"/><span class="kw">then </span>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</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"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c14">z1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:67_4_1_1"><span class="lab"><font color="Green" title="E82">A48</font></span></a></span>;<br/><a NAME="E42:67_4_1_1"/><span class="kw">then </span>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">t9</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">t</font></span>)</span> where <font color="Olive" title="b1">t9</font>, <font color="Olive" title="b2">t</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">t9</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Olive" title="b2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:67_4_1_1"><span class="lab"><font color="Green" title="E80">A46</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">t9</font>, <font color="Maroon" title="c21">t</font> being    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font><span class="kw"> such that </span><br/><a NAME="E44:67_4_1_1"/><span class="lab"><font color="Green" title="E84">A50</font></span>: 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">t9</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c21">t</font>
 <span class="kw">and </span><br/><a NAME="E45:67_4_1_1"/><span class="lab"><font color="Green" title="E85">A51</font></span>: 
<font color="Maroon" title="c20">t9</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E46:67_4_1_1"/><span class="lab"><font color="Green" title="E86">A52</font></span>: 
<font color="Maroon" title="c21">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font>
 ;<br/><a NAME="E47:67_4_1_1"/>
 <a href="termord.html#K5" title="TERMORD:func.5">HM</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="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="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/><a NAME="E48:67_4_1_1"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><span class="kw">then </span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T7" title="POLYNOM7:th.7">POLYNOM7:7</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T22" title="TERMORD:th.22">TERMORD:22</a></span>
;<br/><a NAME="E50:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A53</font></span>: 
<font color="Maroon" title="c20">t9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E45:67_4_1_1"><span class="lab"><font color="Green" title="E85">A51</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E51:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A54</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:67_4_1_1"><span class="lab"><font color="Green" title="E84">A50</font></span></a>, <a class="ref" href="pre_poly.html#T50" title="PRE_POLY:th.50">PRE_POLY:50</a></span>;<br/><a NAME="E52:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A55</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_2.html#D1" title="GROEB_2:def.1">GROEB_2:def 1</a></span>;<br/><span class="lab"><font color="Green" title="E90">A56</font></span>: <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="pre_poly.html#K12" title="PRE_POLY:func.12">+</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="pre_poly.html#K13" title="PRE_POLY:func.13">-'</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="ref" href="pre_poly.html#T48" title="PRE_POLY:th.48">PRE_POLY:48</a></span>
<br/>.= 
<font color="Maroon" title="c21">t</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:67_4_1_1"><span class="lab"><font color="Green" title="E84">A50</font></span></a>, <a class="txt" href="#E50:67_4_1_1"><span class="lab"><font color="Green" title="E87">A53</font></span></a>, <a class="txt" href="#E52:67_4_1_1"><span class="lab"><font color="Green" title="E89">A55</font></span></a>, <a class="ref" href="pre_poly.html#T48" title="PRE_POLY:th.48">PRE_POLY:48</a></span>
;<br/><a NAME="E54:67_4_1_1"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E16:67_4_1_1"><span class="lab"><font color="Green" title="E76">A30</font></span></a>, <a class="ref" href="groeb_3.html#T27" target="_self" title="GROEB_3:th.27">Th27</a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></span>;<br/><a NAME="E55:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A57</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:67_4_1_1"><span class="lab"><font color="Green" title="E79">A45</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E56:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A58</font></span>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <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="termord.html#K6" title="TERMORD:func.6">Red</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="#E46:67_4_1_1"><span class="lab"><font color="Green" title="E86">A52</font></span></a>, <a class="txt" href="#E53:67_4_1_1"><span class="lab"><font color="Green" title="E90">A56</font></span></a></span>;<br/><a NAME="E57:67_4_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>;<br/><a NAME="E58:67_4_1_1"/><span class="kw">then </span>
not <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E59:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A59</font></span>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <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 class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E60:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A60</font></span>: 
<span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <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"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:67_4_1_1"><span class="lab"><font color="Green" title="E92">A58</font></span></a>, <a class="txt" href="#E3:67_4_1_1"><span class="lab"><font color="Green" title="E67">A13</font></span></a>, <a class="ref" href="termord.html#T40" title="TERMORD:th.40">TERMORD:40</a></span>;<br/><div><span class="lab"><font color="Green" title="E95">A61</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_8"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1_1_8"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:67_4_1_1_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A62</font></span>: 
<font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T16" target="_self" title="GROEB_3:th.16">Th16</a></span>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<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"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="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"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<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/>.= 
 <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="#E60:67_4_1_1"><span class="lab"><font color="Green" title="E94">A60</font></span></a>, <a class="txt" href="#E2:67_4_1_1_8"><span class="lab"><font color="Green" title="E96">A62</font></span></a>, <a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></span>
;<br/><span class="kw">hence </span><a NAME="E4:67_4_1_1_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:67_4_1_1"><span class="lab"><font color="Green" title="E86">A52</font></span></a>, <a class="txt" href="#E53:67_4_1_1"><span class="lab"><font color="Green" title="E90">A56</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</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><a NAME="E62:67_4_1_1"/><span class="lab"><font color="Green" title="E96">A63</font></span>: 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D12" title="PRE_POLY:def.12">PRE_POLY:def 12</a></span>;<br/><div><span class="lab"><font color="Green" title="E97">A64</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_9"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1_1_9"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span> <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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:67_4_1_1_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E98">A65</font></span>: 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</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"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:67_4_1_1"><span class="lab"><font color="Green" title="E96">A63</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><a NAME="E3:67_4_1_1_9"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">v</font></span>)</span> where <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">u</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="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Olive" title="b2">v</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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T30" title="TERMORD:th.30">TERMORD:30</a></span>;<br/><a NAME="E4:67_4_1_1_9"/><span class="kw">then </span>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">v</font></span>)</span> where <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">u</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="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Olive" title="b2">v</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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67_4_1_1_9"><span class="lab"><font color="Green" title="E98">A65</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c22">t9</font>, <font color="Maroon" title="c23">t</font> being    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font><span class="kw"> such that </span><br/><a NAME="E6:67_4_1_1_9"/><span class="lab"><font color="Green" title="E99">A66</font></span>: 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">t9</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c23">t</font>
 <span class="kw">and </span><br/><a NAME="E7:67_4_1_1_9"/><span class="lab"><font color="Green" title="E100">A67</font></span>: 
<font color="Maroon" title="c22">t9</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="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E8:67_4_1_1_9"/><span class="lab"><font color="Green" title="E101">A68</font></span>: 
<font color="Maroon" title="c23">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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 ;<br/><a NAME="E9:67_4_1_1_9"/><span class="lab"><font color="Green" title="E102">A69</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">t9</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c23">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:67_4_1_1"><span class="lab"><font color="Green" title="E88">A54</font></span></a>, <a class="txt" href="#E6:67_4_1_1_9"><span class="lab"><font color="Green" title="E99">A66</font></span></a>, <a class="ref" href="groeb_2.html#D1" title="GROEB_2:def.1">GROEB_2:def 1</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_9_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1_1_9_1"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <font color="Maroon" title="c23">t</font>,<font color="Maroon" title="c2">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:67_4_1_1_9_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A70</font></span>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c23">t</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></span>;<br/><a NAME="E3:67_4_1_1_9_1"/>
<font color="Maroon" title="c23">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E8:67_4_1_1_9"><span class="lab"><font color="Green" title="E101">A68</font></span></a>, <a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>;<br/><a NAME="E4:67_4_1_1_9_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E56:67_4_1_1"><span class="lab"><font color="Green" title="E92">A58</font></span></a>, <a class="txt" href="#E3:67_4_1_1"><span class="lab"><font color="Green" title="E67">A13</font></span></a>, <a class="txt" href="#E2:67_4_1_1_9_1"><span class="lab"><font color="Green" title="E103">A70</font></span></a>, <a class="ref" href="groeb_3.html#T24" target="_self" title="GROEB_3:th.24">Th24</a></span>;<br/><span class="kw">hence </span><a NAME="E5:67_4_1_1_9_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:67_4_1_1"><span class="lab"><font color="Green" title="E74">A21</font></span></a>, <a class="txt" href="#E61:67_4_1_1"><span class="lab"><font color="Green" title="E95">A61</font></span></a>, <a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></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><a NAME="E11:67_4_1_1_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A71</font></span>: 
<font color="Maroon" title="c23">t</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T5" title="TERMORD:th.5">TERMORD:5</a></span>;<br/><a NAME="E12:67_4_1_1_9"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c4">p1</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>;<br/><a NAME="E13:67_4_1_1_9"/><span class="kw">then </span>
not <font color="Maroon" title="c22">t9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67_4_1_1_9"><span class="lab"><font color="Green" title="E100">A67</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E14:67_4_1_1_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E104">A72</font></span>: 
<font color="Maroon" title="c22">t9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <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 class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E15:67_4_1_1_9"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c4">p1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T35" title="TERMORD:th.35">TERMORD:35</a></span>;<br/><a NAME="E16:67_4_1_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c22">t9</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <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>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67_4_1_1_9"><span class="lab"><font color="Green" title="E100">A67</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E17:67_4_1_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c22">t9</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <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>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:67_4_1_1_9"><span class="lab"><font color="Green" title="E104">A72</font></span></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></span>;<br/><a NAME="E18:67_4_1_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c23">t</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c22">t9</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="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>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:67_4_1_1_9"><span class="lab"><font color="Green" title="E103">A71</font></span></a>, <a class="ref" href="groeb_3.html#T6" target="_self" title="GROEB_3:th.6">Th6</a></span>;<br/><span class="kw">hence </span><a NAME="E19:67_4_1_1_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67_4_1_1_9"><span class="lab"><font color="Green" title="E102">A69</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="lab"><font color="Green" title="E98">A73</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_10"><span class="kw">now </span></a><div class="add"><a NAME="E1:67_4_1_1_10"/>
 <a href="termord.html#K5" title="TERMORD:func.5">HM</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="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="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/><a NAME="E2:67_4_1_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E99">A74</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E3:67_4_1_1_10"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <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="termord.html#K5" title="TERMORD:func.5">HM</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#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E4:67_4_1_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A75</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="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="termord.html#K5" title="TERMORD:func.5">HM</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#T26" title="TERMORD:th.26">TERMORD:26</a></span>;<br/><a NAME="E5:67_4_1_1_10"/><span class="lab"><font color="Green" title="E101">A76</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">v</font></span>)</span> where <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">u</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Olive" title="b2">v</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="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<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#T30" title="TERMORD:th.30">TERMORD:30</a></span>;<br/><span class="kw">assume </span><a NAME="E6:67_4_1_1_10"/>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</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"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E7:67_4_1_1_10"/><span class="kw">then </span>
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">u</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Olive" title="b2">v</font></span>)</span> where <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> : ( <font color="Olive" title="b1">u</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> &amp; <font color="Olive" title="b2">v</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="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> ) </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:67_4_1_1_10"><span class="lab"><font color="Green" title="E101">A76</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c22">t9</font>, <font color="Maroon" title="c23">t</font> being    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font><span class="kw"> such that </span><br/><a NAME="E9:67_4_1_1_10"/><span class="lab"><font color="Green" title="E102">A77</font></span>: 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">t9</font> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <font color="Maroon" title="c23">t</font>
 <span class="kw">and </span><br/><a NAME="E10:67_4_1_1_10"/><span class="lab"><font color="Green" title="E103">A78</font></span>: 
<font color="Maroon" title="c22">t9</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="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E11:67_4_1_1_10"/><span class="lab"><font color="Green" title="E104">A79</font></span>: 
<font color="Maroon" title="c23">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="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span>
 ;<br/><a NAME="E12:67_4_1_1_10"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> st  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67_4_1_1_10"><span class="lab"><font color="Green" title="E99">A74</font></span></a>, <a class="ref" href="polynom7.html#T6" title="POLYNOM7:th.6">POLYNOM7:6</a></span>;<br/><a NAME="E13:67_4_1_1_10"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67_4_1_1_10"><span class="lab"><font color="Green" title="E100">A75</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E14:67_4_1_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c22">t9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E10:67_4_1_1_10"><span class="lab"><font color="Green" title="E103">A78</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E15:67_4_1_1_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E55:67_4_1_1"><span class="lab"><font color="Green" title="E91">A57</font></span></a>, <a class="txt" href="#E46:67_4_1_1"><span class="lab"><font color="Green" title="E86">A52</font></span></a>, <a class="txt" href="#E52:67_4_1_1"><span class="lab"><font color="Green" title="E89">A55</font></span></a>, <a class="txt" href="#E53:67_4_1_1"><span class="lab"><font color="Green" title="E90">A56</font></span></a>, <a class="txt" href="#E9:67_4_1_1_10"><span class="lab"><font color="Green" title="E102">A77</font></span></a>, <a class="txt" href="#E11:67_4_1_1_10"><span class="lab"><font color="Green" title="E104">A79</font></span></a>, <a class="ref" href="groeb_3.html#T52" target="_self" title="GROEB_3:th.52">Th52</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><span class="kw">set </span><font color="Maroon" title="c22">g</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</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>)</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>;<br/><a NAME="E65:67_4_1_1"/><span class="lab"><font color="Green" title="E99">A80</font></span>: 
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D12" title="PRE_POLY:def.12">PRE_POLY:def 12</a></span>;<br/><span class="lab"><font color="Green" title="E100">A81</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">red1</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</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"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E63:67_4_1_1"><span class="lab"><font color="Green" title="E97">A64</font></span></a>, <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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</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"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:67_4_1_1"><span class="lab"><font color="Green" title="E96">A63</font></span></a>, <a class="txt" href="#E64:67_4_1_1"><span class="lab"><font color="Green" title="E98">A73</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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/><a NAME="E67:67_4_1_1"/>
<font color="Maroon" title="c16">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p2">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T10" target="_self" title="GROEB_3:th.10">Th10</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c23">lowz1w</font> =  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c14">z1</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c16">w</font> as   <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a>  <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T37" target="_self" title="GROEB_3:th.37">Th37</a></span>;<br/><a NAME="E69:67_4_1_1"/>
<font color="Maroon" title="c16">w</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p3">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T10" target="_self" title="GROEB_3:th.10">Th10</a></span>;<br/><a NAME="E70:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A82</font></span>: 
<font color="Maroon" title="c16">w</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E71:67_4_1_1"/>
<font color="Maroon" title="c23">lowz1w</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 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="E72:67_4_1_1"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c23">lowz1w</font> <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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E73:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A83</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c23">lowz1w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c23">lowz1w</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T7" title="POLYNOM7:th.7">POLYNOM7:7</a></span>;<br/><a NAME="E74:67_4_1_1"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c15">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T10" target="_self" title="GROEB_3:th.10">Th10</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="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> = 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c23">lowz1w</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:67_4_1_1"><span class="lab"><font color="Green" title="E81">A47</font></span></a>, <a class="txt" href="#E52:67_4_1_1"><span class="lab"><font color="Green" title="E89">A55</font></span></a>, <a class="ref" href="groeb_3.html#T44" target="_self" title="GROEB_3:th.44">Th44</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c23">lowz1w</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_3.html#T7" target="_self" title="GROEB_3:th.7">Th7</a></span>
<br/>.= 
<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> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c23">lowz1w</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T22" title="TERMORD:th.22">TERMORD:22</a></span>
;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A84</font></span>: <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="p1">(<span class="default"><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> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c23">lowz1w</font></span>)</span></span>)</span> <a href="pre_poly.html#K13" title="PRE_POLY:func.13">-'</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="ref" href="pre_poly.html#T48" title="PRE_POLY:th.48">PRE_POLY:48</a></span>
<br/>.= 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c23">lowz1w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T48" title="PRE_POLY:th.48">PRE_POLY:48</a></span>
;<br/><a NAME="E77:67_4_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c23">lowz1w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:67_4_1_1"><span class="lab"><font color="Green" title="E102">A83</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E78:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E104">A85</font></span>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c14">z1</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c16">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:67_4_1_1"><span class="lab"><font color="Green" title="E101">A82</font></span></a>, <a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>;<br/><a NAME="E79:67_4_1_1"/>
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_14"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E105">A86</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_14_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c24">t</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</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"> ( <font color="Maroon" title="c24">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font> implies <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c24">t</font>,<font color="Maroon" title="c2">T</font> )</span><br/><span class="kw">assume </span><a NAME="E1:67_4_1_1_14_1"/><span class="lab"><font color="Green" title="E106">A87</font></span>: 
<font color="Maroon" title="c24">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c14">z1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c24">t</font>,<font color="Maroon" title="c2">T</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_14_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1_1_14_1_1"/><span class="lab"><font color="Green" title="E107">A88</font></span>: 
<font color="Maroon" title="c24">t</font> <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>,<font color="Maroon" title="c2">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:67_4_1_1_14_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">t</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></span>;<br/><a NAME="E3:67_4_1_1_14_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c14">z1</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c16">w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:67_4_1_1"><span class="lab"><font color="Green" title="E101">A82</font></span></a>, <a class="txt" href="#E78:67_4_1_1"><span class="lab"><font color="Green" title="E104">A85</font></span></a>, <a class="txt" href="#E1:67_4_1_1_14_1"><span class="lab"><font color="Green" title="E106">A87</font></span></a>, <a class="ref" href="groeb_3.html#T24" target="_self" title="GROEB_3:th.24">Th24</a></span>;<br/><a NAME="E4:67_4_1_1_14_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c23">lowz1w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:67_4_1_1"><span class="lab"><font color="Green" title="E101">A82</font></span></a>, <a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>;<br/><a NAME="E5:67_4_1_1_14_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c23">lowz1w</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:67_4_1_1"><span class="lab"><font color="Green" title="E102">A83</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:67_4_1_1_14_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E76:67_4_1_1"><span class="lab"><font color="Green" title="E103">A84</font></span></a>, <a class="txt" href="#E1:67_4_1_1_14_1_1"><span class="lab"><font color="Green" title="E107">A88</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><span class="kw">hence </span><a NAME="E3:67_4_1_1_14_1"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a> <font color="Maroon" title="c24">t</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T5" title="TERMORD:th.5">TERMORD:5</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>
<span class="kw">set </span><font color="Maroon" title="c24">r</font> =  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font>;<br/>
<a NAME="E2:67_4_1_1_14"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67_4_1_1"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="ref" href="groeb_3.html#T42" target="_self" title="GROEB_3:th.42">Th42</a></span>;<br/>
<a NAME="E3:67_4_1_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A89</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E4:67_4_1_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E107">A90</font></span>: 
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<span class="lab"><font color="Green" title="E108">A91</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></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"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <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="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></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"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <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="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></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"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <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="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:67_4_1_1_14"><span class="lab"><font color="Green" title="E107">A90</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <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="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T25" title="RLVECT_1:th.25">RLVECT_1:25</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <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="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></span>
;<br/>
<a NAME="E6:67_4_1_1_14"/><span class="lab"><font color="Green" title="E109">A92</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:67_4_1_1_14"><span class="lab"><font color="Green" title="E106">A89</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E7:67_4_1_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A93</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>;<br/>
<a NAME="E8:67_4_1_1_14"/><span class="lab"><font color="Green" title="E111">A94</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="ref" href="groeb_3.html#T26" target="_self" title="GROEB_3:th.26">Th26</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_14_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1_1_14_3"/><span class="lab"><font color="Green" title="E112">A95</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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 class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div><span class="lab"><font color="Green" title="E113">A96</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_14_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c25">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c25">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font> implies <font color="Maroon" title="c25">u</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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:67_4_1_1_14_3_1"/><span class="lab"><font color="Green" title="E114">A97</font></span>: 
<font color="Maroon" title="c25">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c25">u</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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c26">u9</font> = <font color="Maroon" title="c25">u</font> as    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> ;<br/><a NAME="E3:67_4_1_1_14_3_1"/>
<font color="Maroon" title="c26">u9</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</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="txt" href="#E1:67_4_1_1_14_3"><span class="lab"><font color="Green" title="E112">A95</font></span></a>, <a class="txt" href="#E1:67_4_1_1_14_3_1"><span class="lab"><font color="Green" title="E114">A97</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E4:67_4_1_1_14_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c26">u9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E7:67_4_1_1_14"><span class="lab"><font color="Green" title="E110">A93</font></span></a>, <a class="txt" href="#E1:67_4_1_1_14_3_1"><span class="lab"><font color="Green" title="E114">A97</font></span></a>, <a class="ref" href="groeb_3.html#T24" target="_self" title="GROEB_3:th.24">Th24</a></span>;<br/><span class="kw">hence </span><a NAME="E5:67_4_1_1_14_3_1"/>
<font color="Maroon" title="c25">u</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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></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><a NAME="E3:67_4_1_1_14_3"/>
for <font color="Olive" title="b1">u</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">u</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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span> holds <br/><font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:67_4_1_1_14"><span class="lab"><font color="Green" title="E111">A94</font></span></a></span>;<br/><a NAME="E4:67_4_1_1_14_3"/><span class="kw">then </span>
<font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:67_4_1_1"><span class="lab"><font color="Green" title="E70">A17</font></span></a>, <a class="txt" href="#E2:67_4_1_1_14_3"><span class="lab"><font color="Green" title="E113">A96</font></span></a>, <a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:67_4_1_1_14_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67_4"><span class="lab"><font color="Green" title="E64">A9</font></span></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>
<a NAME="E10:67_4_1_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A98</font></span>: 
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E11:67_4_1_1_14"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><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><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T36" title="TERMORD:th.36">TERMORD:36</a></span>;<br/>
<a NAME="E12:67_4_1_1_14"/><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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</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> <font color="Maroon" title="c7">red2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1_14"><span class="lab"><font color="Green" title="E109">A92</font></span></a>, <a class="txt" href="#E8:67_4_1_1_14"><span class="lab"><font color="Green" title="E111">A94</font></span></a>, <a class="txt" href="#E10:67_4_1_1_14"><span class="lab"><font color="Green" title="E112">A98</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E13:67_4_1_1_14"/><span class="kw">then </span>
<font color="Maroon" title="c14">z1</font> <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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> <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="#E5:67_4_1_1_14"><span class="lab"><font color="Green" title="E108">A91</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/>
<a NAME="E14:67_4_1_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A99</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</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> <font color="Maroon" title="c14">z1</font>
 
<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="E15:67_4_1_1_14"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">red2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T35" title="TERMORD:th.35">TERMORD:35</a></span>;<br/>
<a NAME="E16:67_4_1_1_14"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="groeb_3.html#K4" title="GROEB_3:func.4">Lower_Support</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E56:67_4_1_1"><span class="lab"><font color="Green" title="E92">A58</font></span></a>, <a class="txt" href="#E1:67_4_1_1_14"><span class="lab"><font color="Green" title="E105">A86</font></span></a>, <a class="txt" href="#E7:67_4_1_1_14"><span class="lab"><font color="Green" title="E110">A93</font></span></a>, <a class="txt" href="#E14:67_4_1_1_14"><span class="lab"><font color="Green" title="E113">A99</font></span></a>, <a class="ref" href="groeb_3.html#T24" target="_self" title="GROEB_3:th.24">Th24</a></span>;<br/>
<a NAME="E17:67_4_1_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E114">A100</font></span>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <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_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="groeb_3.html#E32"><span class="lab"><font color="Green" title="E25">Lm3</font></span></a></span>;<br/>
<a NAME="E18:67_4_1_1_14"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span> <a href="xboole_0.html#K4" title="XBOOLE_0:func.4">\</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:67_4_1_1"><span class="lab"><font color="Green" title="E95">A61</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E19:67_4_1_1_14"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67_4_1_1"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="ref" href="groeb_3.html#T42" target="_self" title="GROEB_3:th.42">Th42</a></span>;<br/>
<a NAME="E20:67_4_1_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E115">A101</font></span>: 
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E116">A102</font></span>: <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<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="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T18" title="TERMORD:th.18">TERMORD:18</a></span>
<br/>.= 
<font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:67_4_1_1"><span class="lab"><font color="Green" title="E69">A16</font></span></a>, <a class="txt" href="#E17:67_4_1_1_14"><span class="lab"><font color="Green" title="E114">A100</font></span></a>, <a class="ref" href="groeb_3.html#T31" target="_self" title="GROEB_3:th.31">Th31</a></span>
;<br/>
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font> = 
<span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></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"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></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/>.= 
<font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:67_4_1_1_14"><span class="lab"><font color="Green" title="E116">A102</font></span></a>, <a class="ref" href="termord.html#T18" title="TERMORD:th.18">TERMORD:18</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E23:67_4_1_1_14"/>
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:67_4_1_1_14"><span class="lab"><font color="Green" title="E115">A101</font></span></a>, <a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</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><span class="kw">then </span><span class="lab"><font color="Green" title="E105">A103</font></span>:  <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font> = 
<span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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 class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T38" title="TERMORD:th.38">TERMORD:38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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 class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67_4_1_1"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="ref" href="groeb_3.html#T43" target="_self" title="GROEB_3:th.43">Th43</a></span>
;<br/><a NAME="E81:67_4_1_1"/><span class="lab"><font color="Green" title="E106">A104</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c14">z1</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span> <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="#E40:67_4_1_1"><span class="lab"><font color="Green" title="E83">A49</font></span></a>, <a class="txt" href="#E36:67_4_1_1"><span class="lab"><font color="Green" title="E82">A48</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1_16"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:67_4_1_1_16"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <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"> contradiction</span><br/><a NAME="E2:67_4_1_1_16"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c14">z1</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E66:67_4_1_1"><span class="lab"><font color="Green" title="E100">A81</font></span></a>, <a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></span>;<br/><span class="kw">hence </span><a NAME="E3:67_4_1_1_16"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E81:67_4_1_1"><span class="lab"><font color="Green" title="E106">A104</font></span></a>, <a class="ref" href="rlvect_1.html#T25" title="RLVECT_1:th.25">RLVECT_1:25</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><a NAME="E83:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E107">A105</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;  <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:67_4_1_1"><span class="lab"><font color="Green" title="E96">A63</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a>, <a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a></span>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</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"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">red1</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<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#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"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:67_4_1_1"><span class="lab"><font color="Green" title="E75">A29</font></span></a>, <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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</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="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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:67_4_1_1"><span class="lab"><font color="Green" title="E77">A40</font></span></a>, <a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1:def 22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c6">red1</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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>)</span> <a href="pre_poly.html#K12" title="PRE_POLY:func.12">+</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">red1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></span>
;<br/><a NAME="E85:67_4_1_1"/><span class="kw">then </span>
<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="termord.html#K5" title="TERMORD:func.5">HM</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>)</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="c6">red1</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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67_4_1_1"><span class="lab"><font color="Green" title="E66">A12</font></span></a>, <a class="txt" href="#E65:67_4_1_1"><span class="lab"><font color="Green" title="E99">A80</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><a NAME="E86:67_4_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E87:67_4_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</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>)</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>, <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:67_4_1_1"><span class="lab"><font color="Green" title="E89">A55</font></span></a>, <a class="txt" href="#E83:67_4_1_1"><span class="lab"><font color="Green" title="E107">A105</font></span></a>, <a class="ref" href="polyred.html#D5" title="POLYRED:def.5">POLYRED:def 5</a></span>;<br/><a NAME="E88:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E108">A106</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</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>)</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D6" title="POLYRED:def.6">POLYRED:def 6</a></span>;<br/><a NAME="E89:67_4_1_1"/>
<font color="Maroon" title="c4">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E90:67_4_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</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>)</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>,<span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E88:67_4_1_1"><span class="lab"><font color="Green" title="E108">A106</font></span></a>, <a class="ref" href="polyred.html#D7" title="POLYRED:def.7">POLYRED:def 7</a></span>;<br/><a NAME="E91:67_4_1_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</a> <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></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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="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></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D13" title="POLYRED:def.13">POLYRED:def 13</a></span>;<br/><a NAME="E92:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E109">A107</font></span>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</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>)</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T16" title="REWRITE1:th.16">REWRITE1:16</a></span>;<br/><a NAME="E93:67_4_1_1"/>
<font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:67_4_1_1"><span class="lab"><font color="Green" title="E71">A18</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E94:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A108</font></span>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67_4_1"><span class="lab"><font color="Green" title="E65">A10</font></span></a>, <a class="txt" href="#E11:67_4_1_1"><span class="lab"><font color="Green" title="E72">A19</font></span></a></span>;<br/><span class="lab"><font color="Green" title="E111">A109</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="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</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="ref" href="termord.html#T26" title="TERMORD:th.26">TERMORD:26</a></span>
<br/>.= 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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/><a NAME="E96:67_4_1_1"/>
<span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> is    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D12" title="PRE_POLY:def.12">PRE_POLY:def 12</a></span>;<br/><a NAME="E97:67_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A110</font></span>: 
<span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#R1" title="HIDDEN:pred.1">=</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="#E61:67_4_1_1"><span class="lab"><font color="Green" title="E95">A61</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="pre_poly.html#K12" title="PRE_POLY:func.12">+</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:67_4_1_1"><span class="lab"><font color="Green" title="E88">A54</font></span></a>, <a class="ref" href="groeb_2.html#D1" title="GROEB_2:def.1">GROEB_2:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></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> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="txt" href="#E95:67_4_1_1"><span class="lab"><font color="Green" title="E111">A109</font></span></a>, <a class="ref" href="polyred.html#T7" title="POLYRED:th.7">POLYRED:7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">p1</font> <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> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#T18" title="TERMORD:th.18">TERMORD:18</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"><span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#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> <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"><span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 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"><span class="p2">(<span class="default"><font color="Maroon" title="c7">red2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<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"><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"><span class="p2">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:67_4_1_1"><span class="lab"><font color="Green" title="E92">A58</font></span></a>, <a class="txt" href="#E3:67_4_1_1"><span class="lab"><font color="Green" title="E67">A13</font></span></a>, <a class="txt" href="#E59:67_4_1_1"><span class="lab"><font color="Green" title="E93">A59</font></span></a>, <a class="ref" href="termord.html#T40" title="TERMORD:th.40">TERMORD:40</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"><span class="p2">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></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> <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"><span class="p2">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E97:67_4_1_1"><span class="lab"><font color="Green" title="E112">A110</font></span></a>, <a class="ref" href="rlvect_1.html#T25" title="RLVECT_1:th.25">RLVECT_1:25</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"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></span>
;<br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</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>)</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> = 
<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="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="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</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>)</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E66:67_4_1_1"><span class="lab"><font color="Green" title="E100">A81</font></span></a>, <a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">VECTSP_1:41</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="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="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D23" title="VECTSP_1:def.23">VECTSP_1:def 23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</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="group_1.html#K8" title="GROUP_1:func.8">*</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="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Maroon" title="c3">L</font></span>)</span></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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D16" title="VECTSP_1:def.16">VECTSP_1:def 16</a></span>
;<br/><span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">/</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>)</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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></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"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T9" title="POLYRED:th.9">POLYRED:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="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="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T30" title="RLVECT_1:th.30">RLVECT_1:30</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#K12" title="POLYNOM1:func.12">*'</a> <font color="Maroon" title="c4">p1</font></span>)</span>
<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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#T38" title="TERMORD:th.38">TERMORD:38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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="polynom1.html#T85" title="POLYNOM1:th.85">POLYNOM1:85</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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="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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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#K6" title="POLYNOM1:func.6">+</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"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<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#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<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#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T6" title="POLYRED:th.6">POLYRED:6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p0">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>)</span></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p5">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</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="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<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#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p0">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<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#T85" title="POLYNOM1:th.85">POLYNOM1:85</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p4">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E80:67_4_1_1"><span class="lab"><font color="Green" title="E105">A103</font></span></a>, <a class="ref" href="polynom1.html#T85" title="POLYNOM1:th.85">POLYNOM1:85</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p0">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p0">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p0">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> <span class="p5">(<span class="default"><font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c17">lowzw</font></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="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T1" title="POLYRED:th.1">POLYRED:1</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p4">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p5">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E80:67_4_1_1"><span class="lab"><font color="Green" title="E105">A103</font></span></a>, <a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p5">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p0">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T1" title="POLYRED:th.1">POLYRED:1</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p5">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T6" title="POLYRED:th.6">POLYRED:6</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></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="kw">hence </span><a NAME="E101:67_4_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c11">m</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E92:67_4_1_1"><span class="lab"><font color="Green" title="E109">A107</font></span></a>, <a class="txt" href="#E94:67_4_1_1"><span class="lab"><font color="Green" title="E110">A108</font></span></a>, <a class="ref" href="rewrite1.html#T17" title="REWRITE1:th.17">REWRITE1:17</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><span class="kw">hence </span><a NAME="E3:67_4_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 ; <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>
<span class="kw">hence </span><a NAME="E4:67_4"/>
(  not <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font>] or <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c10">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )
 ; <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>
<a NAME="E17:67"/><span class="lab"><font color="Green" title="E64">A111</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span> &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67_5"/>
<font color="Maroon" title="c10">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c5">p2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:67_5"/><span class="lab"><font color="Green" title="E65">A112</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span><br/>

<a NAME="E3:67_5"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="#E2:67_5"><span class="lab"><font color="Green" title="E65">A112</font></span></a></span>;<br/>
<a NAME="E4:67_5"/><span class="kw">then </span>
 <a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><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>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T4" title="POLYRED:th.4">POLYRED:4</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><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>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T5" title="POLYRED:th.5">POLYRED:5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T2" title="POLYRED:th.2">POLYRED:2</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:67_5"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p4">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="groeb_3.html#K6" title="GROEB_3:func.6">Low</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c10">m</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T13" title="REWRITE1:th.13">REWRITE1:13</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>
<a NAME="E18:67"/>
for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">j9</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="int_1.html#S7" title="INT_1:sch.7">INT_1:sch 7</a>(<a class="txt" href="#E17:67"><span class="lab"><font color="Green" title="E64">A111</font></span></a>, <a class="txt" href="#E16:67"><span class="lab"><font color="Green" title="E63">A8</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E19:67"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> <span class="p1"><a href="groeb_1.html#K1" title="GROEB_1:func.1">{</a><span class="default"><font color="Maroon" title="c4">p1</font></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>,<font color="Maroon" title="c2">T</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c4">p1</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</a> <font color="Maroon" title="c5">p2</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">p2</font> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><a href="termord.html#K6" title="TERMORD:func.6">Red</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="#E5:67"><span class="lab"><font color="Green" title="E58">A3</font></span></a>, <a class="txt" href="#E15:67"><span class="lab"><font color="Green" title="E62">A7</font></span></a>, <a class="txt" href="#E8:67"><span class="lab"><font color="Green" title="E59">A4</font></span></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>
