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<span class="kw">let </span><font color="Maroon" title="c1">n</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="firebrick">::  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#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="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">P</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>)</span>)</span>  st (  for <font color="Olive" title="b4">p1</font>, <font color="Olive" title="b5">p2</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>  st <font color="Olive" title="b4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">p2</font> &amp; <font color="Olive" title="b4">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">P</font> &amp; <font color="Olive" title="b5">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">P</font> holds <br/> for <font color="Olive" title="b6">m1</font>, <font color="Olive" title="b7">m2</font> being   <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>  st  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b6">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b4">p1</font></span>)</span>,<font color="Olive" title="b1">T</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b7">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b5">p2</font></span>)</span>,<font color="Olive" title="b1">T</font>) holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Olive" title="b3">P</font>,<font color="Olive" title="b1">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b4">p1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b5">p2</font></span>)</span>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>) ) holds <br/><font color="Olive" title="b3">P</font> <a href="groeb_1.html#R1" title="GROEB_1:pred.1">is_Groebner_basis_wrt</a> <font color="Olive" title="b1">T</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">T</font> be   <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>   <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="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">P</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>)</span>)</span>  st (  for <font color="Olive" title="b3">p1</font>, <font color="Olive" title="b4">p2</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>  st <font color="Olive" title="b3">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">p2</font> &amp; <font color="Olive" title="b3">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b4">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">P</font> holds <br/> for <font color="Olive" title="b5">m1</font>, <font color="Olive" title="b6">m2</font> being   <a href="polynom7.html#NM1" title="POLYNOM7:NM.1">Monomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>  st  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b5">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b3">p1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b6">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b4">p2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Olive" title="b2">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b3">p1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b4">p2</font></span>)</span>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>) ) holds <br/><font color="Olive" title="b2">P</font> <a href="groeb_1.html#R1" title="GROEB_1:pred.1">is_Groebner_basis_wrt</a> <font color="Maroon" title="c2">T</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span>  st (  for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  st <font color="Olive" title="b2">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">p2</font> &amp; <font color="Olive" title="b2">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b3">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">P</font> holds <br/> for <font color="Olive" title="b4">m1</font>, <font color="Olive" title="b5">m2</font> being   <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>  st  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b2">p1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b5">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b3">p2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Olive" title="b1">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b2">p1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b3">p2</font></span>)</span>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) ) holds <br/><font color="Olive" title="b1">P</font> <a href="groeb_1.html#R1" title="GROEB_1:pred.1">is_Groebner_basis_wrt</a> <font color="Maroon" title="c2">T</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">P</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  st <font color="Olive" title="b1">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">p2</font> &amp; <font color="Olive" title="b1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b2">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> holds <br/> for <font color="Olive" title="b3">m1</font>, <font color="Olive" title="b4">m2</font> being   <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>  st  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b1">p1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b2">p2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b1">p1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b2">p2</font></span>)</span>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) ) implies <font color="Maroon" title="c4">P</font> <a href="groeb_1.html#R1" title="GROEB_1:pred.1">is_Groebner_basis_wrt</a> <font color="Maroon" title="c2">T</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:26"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
 for <font color="Olive" title="b1">p1</font>, <font color="Olive" title="b2">p2</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  st <font color="Olive" title="b1">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">p2</font> &amp; <font color="Olive" title="b1">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b2">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> holds <br/> for <font color="Olive" title="b3">m1</font>, <font color="Olive" title="b4">m2</font> being   <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>  st  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b1">p1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b2">p2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) holds <br/> <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b1">p1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Olive" title="b2">p2</font></span>)</span>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">P</font> <a href="groeb_1.html#R1" title="GROEB_1:pred.1">is_Groebner_basis_wrt</a> <font color="Maroon" title="c2">T</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">R</font> =  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>);<br/>
<a NAME="E2:26"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</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="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c8">c</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></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> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font></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> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) implies <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26_1"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></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> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">and </span><br/><a NAME="E2:26_1"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font></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> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)</span><br/><span class="kw">consider </span><font color="Maroon" title="c9">f</font>, <font color="Maroon" title="c10">f1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:26_1"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c9">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:26_1"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon" title="c10">f1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:26_1"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">f</font>,<font color="Maroon" title="c10">f1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/><a NAME="E7:26_1"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
 not <font color="Maroon" title="c9">f</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"><span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span><a href="groeb_1.html#K1" title="GROEB_1:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c11">f</font> = <font color="Maroon" title="c9">f</font> as   <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="#E4:26_1"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>;<br/><a NAME="E9:26_1"/>
<font color="Maroon" title="c11">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:26_1"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">f</font> = <font color="Maroon" title="c11">f</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="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">f1</font> = <font color="Maroon" title="c10">f1</font> as   <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="#E5:26_1"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="ref" href="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>;<br/><a NAME="E12:26_1"/>
<font color="Maroon" title="c12">f</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Maroon" title="c13">f1</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E6:26_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="polyred.html#D13" title="POLYRED:def.13">POLYRED:def 13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">g1</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font><span class="kw"> such that </span><br/><a NAME="E14:26_1"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<font color="Maroon" title="c14">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font>
 <span class="kw">and </span><br/><a NAME="E15:26_1"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c12">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Maroon" title="c13">f1</font>,<font color="Maroon" title="c14">g1</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D7" title="POLYRED:def.7">POLYRED:def 7</a></span>;<br/><a NAME="E16:26_1"/>
 ex <font color="Olive" title="b1">b1</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> st <font color="Maroon" title="c12">f</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <font color="Maroon" title="c13">f1</font>,<font color="Maroon" title="c14">g1</font>,<font color="Olive" title="b1">b1</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:26_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="ref" href="polyred.html#D6" title="POLYRED:def.6">POLYRED:def 6</a></span>;<br/><a NAME="E17:26_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A11</font></span>: 
<font color="Maroon" title="c14">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polyred.html#D5" title="POLYRED:def.5">POLYRED:def 5</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c15">f9</font>, <font color="Maroon" title="c16">f2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E19:26_1"/>
<font color="Maroon" title="c15">f9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E20:26_1"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
<font color="Maroon" title="c16">f2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E21:26_1"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c15">f9</font>,<font color="Maroon" title="c16">f2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c17">f2</font> = <font color="Maroon" title="c16">f2</font> as   <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="#E20:26_1"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>;<br/><span class="lab"><font color="Green" title="E28">A14</font></span>: <font color="Maroon" title="c17">f2</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:26_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c8">c</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></span>
;<br/><span class="kw">reconsider </span><font color="Maroon" title="c18">g1</font> = <font color="Maroon" title="c14">g1</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="#E17:26_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c19">m1</font> being   <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"> such that </span><br/><a NAME="E26:26_1"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
<font color="Maroon" title="c13">f1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c12">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E27:26_1"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
 not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c13">f1</font>
 <span class="kw">and </span><br/><a NAME="E28:26_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c12">f</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="#E15:26_1"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="ref" href="groeb_1.html#T2" title="GROEB_1:th.2">GROEB_1:2</a></span>;<br/><span class="lab"><font color="Green" title="E31">A17</font></span>: <font color="Maroon" title="c15">f9</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:26_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c6">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
;<br/><span class="lab"><font color="Green" title="E32">A18</font></span>: <font color="Maroon" title="c15">f9</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:26_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c6">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c12">f</font>,<font color="Maroon" title="c13">f1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:26_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D1" title="MCART_1:def.1">MCART_1:def 1</a></span>
;<br/><a NAME="E31:26_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">f</font> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a> <font color="Maroon" title="c17">f2</font>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E21:26_1"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="polyred.html#D13" title="POLYRED:def.13">POLYRED:def 13</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">g2</font> being   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font><span class="kw"> such that </span><br/><a NAME="E33:26_1"/><span class="lab"><font color="Green" title="E33">A19</font></span>: 
<font color="Maroon" title="c20">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font>
 <span class="kw">and </span><br/><a NAME="E34:26_1"/><span class="lab"><font color="Green" title="E34">A20</font></span>: 
<font color="Maroon" title="c12">f</font> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a> <font color="Maroon" title="c17">f2</font>,<font color="Maroon" title="c20">g2</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#D7" title="POLYRED:def.7">POLYRED:def 7</a></span>;<br/><a NAME="E35:26_1"/>
 ex <font color="Olive" title="b1">b2</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> st <font color="Maroon" title="c12">f</font> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a> <font color="Maroon" title="c17">f2</font>,<font color="Maroon" title="c20">g2</font>,<font color="Olive" title="b1">b2</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:26_1"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="polyred.html#D6" title="POLYRED:def.6">POLYRED:def 6</a></span>;<br/><a NAME="E36:26_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A21</font></span>: 
<font color="Maroon" title="c20">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polyred.html#D5" title="POLYRED:def.5">POLYRED:def 5</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c21">g2</font> = <font color="Maroon" title="c20">g2</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="ref" href="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c22">m2</font> being   <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"> such that </span><br/><a NAME="E39:26_1"/><span class="lab"><font color="Green" title="E36">A22</font></span>: 
<font color="Maroon" title="c17">f2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c12">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E40:26_1"/><span class="lab"><font color="Green" title="E37">A23</font></span>: 
 not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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#K2" title="POLYNOM1:func.2">Support</a> <font color="Maroon" title="c17">f2</font>
 <span class="kw">and </span><br/><a NAME="E41:26_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c12">f</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="#E34:26_1"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="groeb_1.html#T2" title="GROEB_1:th.2">GROEB_1:2</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c23">mg1</font> = <font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font>;<br/><span class="kw">set </span><font color="Maroon" title="c24">mg2</font> = <font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font>;<br/><span class="lab"><font color="Green" title="E38">A24</font></span>: <font color="Maroon" title="c13">f1</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:26_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c7">b</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#D2" title="MCART_1:def.2">MCART_1:def 2</a></span>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_5"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_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="E1:26_1_5_1"/>
( <font color="Maroon" title="c19">m1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) or <font color="Maroon" title="c22">m2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) or ( <font color="Maroon" title="c19">m1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) &amp; <font color="Maroon" title="c22">m2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_1"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_1"/>
<font color="Maroon" title="c19">m1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)</span><br/><div class="add"><span class="kw">then </span><font color="Maroon" title="c13">f1</font> = 
<font color="Maroon" title="c12">f</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">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="txt" href="#E26:26_1"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="ref" href="polyred.html#T5" title="POLYRED:th.5">POLYRED:5</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T4" title="POLYRED:th.4">POLYRED:4</a></span>
;<br/><a NAME="E3:26_1_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A25</font></span>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E30:26_1"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E42:26_1"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E29:26_1"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="rewrite1.html#T15" title="REWRITE1:th.15">REWRITE1:15</a></span>;<br/><a NAME="E4:26_1_5_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T12" title="REWRITE1:th.12">REWRITE1:12</a></span>;<br/><span class="kw">hence </span><a NAME="E5:26_1_5_1_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26_1_5_1_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="rewrite1.html#D7" title="REWRITE1:def.7">REWRITE1:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="26_1_5_1_2"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_2"/>
<font color="Maroon" title="c22">m2</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)</span><br/><div class="add"><span class="kw">then </span><font color="Maroon" title="c17">f2</font> = 
<font color="Maroon" title="c12">f</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">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="txt" href="#E39:26_1"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="polyred.html#T5" title="POLYRED:th.5">POLYRED:5</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T4" title="POLYRED:th.4">POLYRED:4</a></span>
;<br/><a NAME="E3:26_1_5_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A26</font></span>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c7">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E30:26_1"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E23:26_1"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E29:26_1"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="rewrite1.html#T15" title="REWRITE1:th.15">REWRITE1:15</a></span>;<br/><a NAME="E4:26_1_5_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c7">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T12" title="REWRITE1:th.12">REWRITE1:12</a></span>;<br/><span class="kw">hence </span><a NAME="E5:26_1_5_1_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26_1_5_1_2"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="ref" href="rewrite1.html#D7" title="REWRITE1:def.7">REWRITE1:def 7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="26_1_5_1_3"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3"/>
( <font color="Maroon" title="c19">m1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) &amp; <font color="Maroon" title="c22">m2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)</span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c25">m1</font> = <font color="Maroon" title="c19">m1</font>, <font color="Maroon" title="c26">m2</font> = <font color="Maroon" title="c22">m2</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="polynom7.html#D1" title="POLYNOM7:def.1">POLYNOM7:def 1</a></span>;<br/><a NAME="E3:26_1_5_1_3"/>
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c18">g1</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#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T29" title="TERMORD:th.29">TERMORD:29</a></span>;<br/><a NAME="E4:26_1_5_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A27</font></span>: 
<font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="E5:26_1_5_1_3"/>
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c21">g2</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#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T29" title="TERMORD:th.29">TERMORD:29</a></span>;<br/><a NAME="E6:26_1_5_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A28</font></span>: 
<font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="E7:26_1_5_1_3"/><span class="lab"><font color="Green" title="E41">A29</font></span>: 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c21">g2</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 ;<br/><a NAME="E8:26_1_5_1_3"/><span class="lab"><font color="Green" title="E42">a1</font></span>: 
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T19" title="POLYNOM1:th.19">POLYNOM1:19</a></span>;<br/><span class="lab"><font color="Green" title="E43">A30</font></span>: <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:26_1"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E39:26_1"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p3">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c12">f</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></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/>.= 
<font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c12">f</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:26_1_5_1_3"><span class="lab"><font color="Green" title="E42">a1</font></span></a>, <a class="ref" href="polynom1.html#T21" title="POLYNOM1:th.21">POLYNOM1:21</a></span>
<br/>.= 
<font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c12">f</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T21" title="POLYNOM1:th.21">POLYNOM1:21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c12">f</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T21" title="POLYNOM1:th.21">POLYNOM1:21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T3" title="POLYRED:th.3">POLYRED:3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
;<br/><a NAME="E10:26_1_5_1_3"/><span class="lab"><font color="Green" title="E44">A31</font></span>: 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c18">g1</font>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
 ;<br/><a NAME="E11:26_1_5_1_3"/><span class="lab"><font color="Green" title="E45">a1</font></span>: 
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T19" title="POLYNOM1:th.19">POLYNOM1:19</a></span>;<br/><a NAME="E12:26_1_5_1_3"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_5_1_3_2"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_5_1_3_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_3_2_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="E1:26_1_5_1_3_2_1_1"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) or <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:26_1_5_1_3_2_1_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:26_1_5_1_3"><span class="lab"><font color="Green" title="E43">A30</font></span></a>, <a class="ref" href="rewrite1.html#T12" title="REWRITE1:th.12">REWRITE1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="26_1_5_1_3_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3_2_1_1_2"/><span class="lab"><font color="Green" title="E46">A32</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_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="E1:26_1_5_1_3_2_1_1_2_1_1"/>
( <font color="Maroon" title="c18">g1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c21">g2</font> or <font color="Maroon" title="c18">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">g2</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3_2_1_1_2_1_1_1"/>
<font color="Maroon" title="c18">g1</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <font color="Maroon" title="c21">g2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span><br/><div class="add"><span class="kw">then </span><font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c26">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:26_1_5_1_3"><span class="lab"><font color="Green" title="E43">A30</font></span></a>, <a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">g1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c25">m1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c26">m2</font></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></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"><font color="Maroon" title="c25">m1</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c26">m2</font></span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T26" title="POLYNOM1:th.26">POLYNOM1:26</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:26_1_5_1_3_2_1_1_2_1_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:26_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="polyred.html#T45" title="POLYRED:th.45">POLYRED:45</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="26_1_5_1_3_2_1_1_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3_2_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E47">A33</font></span>: 
<font color="Maroon" title="c18">g1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">g2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1_1_2_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="E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1"/>
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) or  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1_1_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1"/><span class="lab"><font color="Green" title="E48">A34</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1_1_2_1_1_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="E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1"/>
(  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span><br/><div class="add"><a NAME="E2:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
 not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T5" title="TERMORD:th.5">TERMORD:5</a></span>;<br/><a NAME="E3:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
 not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="E4:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A35</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></span>;<br/><span class="lab"><font color="Green" title="E50">A36</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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#T15" title="POLYNOM1:th.15">POLYNOM1:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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#T17" title="POLYNOM1:th.17">POLYNOM1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="txt" href="#E4:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="rlvect_1.html#T12" title="RLVECT_1:th.12">RLVECT_1:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a></span>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</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="E6:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="#E4:26_1_5_1_3"><span class="lab"><font color="Green" title="E39">A27</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>;<br/><a NAME="E7:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A37</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></span>;<br/><a NAME="E8:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E52">A38</font></span>: 
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c18">g1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</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/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</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="c18">g1</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"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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"><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="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c18">g1</font>,<font color="Maroon" title="c2">T</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="c18">g1</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"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E50">A36</font></span></a>, <a class="ref" href="termord.html#T32" title="TERMORD:th.32">TERMORD:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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"><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="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c18">g1</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="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="c18">g1</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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D11" title="VECTSP_1:def.11">VECTSP_1:def 11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c25">m1</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="c18">g1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c18">g1</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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" title="GROUP_1:def.3">GROUP_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c25">m1</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="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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:26_1_5_1_3"><span class="lab"><font color="Green" title="E44">A31</font></span></a>, <a class="ref" href="vectsp_1.html#D10" title="VECTSP_1:def.10">VECTSP_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D8" title="VECTSP_1:def.8">VECTSP_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> (<span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> (<span class="p3">(<span class="default"><a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <font color="Maroon" title="c25">m1</font></span>)</span>,<span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c25">m1</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> (<span class="p3">(<span class="default"><a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <font color="Maroon" title="c25">m1</font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c25">m1</font></span>)</span>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T11" title="POLYNOM7:th.11">POLYNOM7:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T21" title="POLYNOM1:th.21">POLYNOM1:21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T3" title="POLYRED:th.3">POLYRED:3</a></span>
<br/>.= 
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></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/><a NAME="E10:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c18">g1</font>, <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="#E17:26_1"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E1:26_1_5_1_3_2_1_1_2"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="txt" href="#E7:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E51">A37</font></span></a>, <a class="txt" href="#E8:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E52">A38</font></span></a>, <a class="ref" href="polyred.html#D5" title="POLYRED:def.5">POLYRED:def 5</a></span>;<br/><a NAME="E11:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c18">g1</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="E12:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:26_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="polyred.html#D7" title="POLYRED:def.7">POLYRED:def 7</a></span>;<br/><a NAME="E13:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_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"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></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> (<font color="Maroon" title="c4">P</font>,<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="E14:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A39</font></span>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>, <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T15" title="REWRITE1:th.15">REWRITE1:15</a></span>;<br/><a NAME="E15:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c26">m2</font></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:26_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="polyred.html#T45" title="POLYRED:th.45">POLYRED:45</a></span>;<br/><a NAME="E16:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/><span class="kw">then </span>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polyred.html#T6" title="POLYRED:th.6">POLYRED:6</a></span>;<br/><span class="kw">hence </span><a NAME="E17:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:26_1_5_1_3"><span class="lab"><font color="Green" title="E43">A30</font></span></a>, <a class="txt" href="#E14:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E53">A39</font></span></a>, <a class="ref" href="rewrite1.html#T16" title="REWRITE1:th.16">REWRITE1:16</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/>
 not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span><br/><div class="add"><a NAME="E2:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T5" title="TERMORD:th.5">TERMORD:5</a></span>;<br/><a NAME="E3:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R2" title="TERMORD:pred.2">&lt;</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="#E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E48">A34</font></span></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></span>;<br/><a NAME="E4:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
 not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>),<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T5" title="TERMORD:th.5">TERMORD:5</a></span>;<br/><a NAME="E5:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
 not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="E6:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A40</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></span>;<br/><span class="lab"><font color="Green" title="E50">A41</font></span>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>)</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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#T15" title="POLYNOM1:th.15">POLYNOM1:15</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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#T17" title="POLYNOM1:th.17">POLYNOM1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="txt" href="#E6:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E49">A40</font></span></a>, <a class="ref" href="rlvect_1.html#T12" title="RLVECT_1:th.12">RLVECT_1:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a></span>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</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="E8:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="#E6:26_1_5_1_3"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>;<br/><a NAME="E9:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A42</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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#K2" title="POLYNOM1:func.2">Support</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c27">x</font> =  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</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="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>;<br/><a NAME="E11:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E52">A43</font></span>: 
<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c21">g2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</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/><span class="kw">reconsider </span><font color="Maroon" title="c28">x</font> = <font color="Maroon" title="c27">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> ;<br/><a NAME="E13:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A44</font></span>: <font color="Maroon" title="c28">x</font> <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> <span class="p2">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>
<br/>.= 
 <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polyred.html#T3" title="POLYRED:th.3">POLYRED:3</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</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="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>
;<br/><div><span class="lab"><font color="Green" title="E54">A45</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2_3"/><span class="kw">then </span>
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>;<br/><a NAME="E3:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">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#T1" title="POLYRED:th.1">POLYRED:1</a></span>;<br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> = 
 <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> <span class="p2">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</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="txt" href="#E11:26_1_5_1_3"><span class="lab"><font color="Green" title="E45">a1</font></span></a>, <a class="txt" href="#E14:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A44</font></span></a>, <a class="ref" href="rlvect_1.html#T6" title="RLVECT_1:th.6">RLVECT_1:6</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</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="rlvect_1.html#T12" title="RLVECT_1:th.12">RLVECT_1:12</a></span>
<br/>.= 
 <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polynom1.html#D10" title="POLYNOM1:def.10">POLYNOM1:def 10</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_5_1_3_2_1_1_2"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p4">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</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="c21">g2</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"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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"><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="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c21">g2</font>,<font color="Maroon" title="c2">T</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="c21">g2</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"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A41</font></span></a>, <a class="ref" href="termord.html#T32" title="TERMORD:th.32">TERMORD:32</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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"><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="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p4">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c21">g2</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="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="c21">g2</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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D11" title="VECTSP_1:def.11">VECTSP_1:def 11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c26">m2</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="c21">g2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c21">g2</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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" title="GROUP_1:def.3">GROUP_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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"><span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c26">m2</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="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="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:26_1_5_1_3"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="ref" href="vectsp_1.html#D10" title="VECTSP_1:def.10">VECTSP_1:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polynom7.html#K5" title="POLYNOM7:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span> <a href="polyred.html#K1" title="POLYRED:func.1">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D8" title="VECTSP_1:def.8">VECTSP_1:def 8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> (<span class="p3">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> (<span class="p3">(<span class="default"><a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <font color="Maroon" title="c26">m2</font></span>)</span>,<span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<font color="Maroon" title="c26">m2</font>,<font color="Maroon" title="c2">T</font>)</span>)</span>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> (<span class="p3">(<span class="default"><a href="polynom7.html#K3" title="POLYNOM7:func.3">coefficient</a> <font color="Maroon" title="c26">m2</font></span>)</span>,<span class="p3">(<span class="default"><a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <font color="Maroon" title="c26">m2</font></span>)</span>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T23" title="TERMORD:th.23">TERMORD:23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T11" title="POLYNOM7:th.11">POLYNOM7:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T21" title="POLYNOM1:th.21">POLYNOM1:21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T3" title="POLYRED:th.3">POLYRED:3</a></span>
<br/>.= 
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></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/><a NAME="E17:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polyred.html#R3" title="POLYRED:pred.3">reduces_to</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c21">g2</font>, <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="#E36:26_1"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E9:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E51">A42</font></span></a>, <a class="txt" href="#E11:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A43</font></span></a>, <a class="txt" href="#E15:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E54">A45</font></span></a>, <a class="ref" href="polyred.html#D5" title="POLYRED:def.5">POLYRED:def 5</a></span>;<br/><a NAME="E18:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polyred.html#R4" title="POLYRED:pred.4">reduces_to</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c21">g2</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="E19:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polyred.html#R5" title="POLYRED:pred.5">reduces_to</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:26_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="polyred.html#D7" title="POLYRED:def.7">POLYRED:def 7</a></span>;<br/><a NAME="E20:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><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"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></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> (<font color="Maroon" title="c4">P</font>,<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="E21:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A46</font></span>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>, <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T15" title="REWRITE1:th.15">REWRITE1:15</a></span>;<br/><span class="lab"><font color="Green" title="E56">A47</font></span>:  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> = 
 <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><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> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</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="polynom7.html#T20" title="POLYNOM7:th.20">POLYNOM7:20</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"><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#K4" title="POLYNOM7:func.4">|</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_2.html#T16" target="_self" title="GROEB_2:th.16">Th20</a></span>
;<br/><a NAME="E23:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Maroon" title="c25">m1</font></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:26_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="ref" href="polyred.html#T45" title="POLYRED:th.45">POLYRED:45</a></span>;<br/><a NAME="E24:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a>  <a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">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="polyred.html#T6" title="POLYRED:th.6">POLYRED:6</a></span>;<br/><a NAME="E25:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E55">A46</font></span></a>, <a class="ref" href="rewrite1.html#T16" title="REWRITE1:th.16">REWRITE1:16</a></span>;<br/><a NAME="E26:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A48</font></span>: 
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">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="txt" href="#E22:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E56">A47</font></span></a>, <a class="ref" href="polyred.html#T47" title="POLYRED:th.47">POLYRED:47</a></span>;<br/><span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T26" title="POLYNOM1:th.26">POLYNOM1:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></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"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span></span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></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"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p3">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></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"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></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"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K8" title="POLYNOM1:func.8">1_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span>)</span> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:26_1_5_1_3"><span class="lab"><font color="Green" title="E45">a1</font></span></a>, <a class="ref" href="polynom1.html#T30" title="POLYNOM1:th.30">POLYNOM1:30</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T30" title="POLYNOM1:th.30">POLYNOM1:30</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>
;<br/><span class="kw">hence </span><a NAME="E28:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:26_1_5_1_3"><span class="lab"><font color="Green" title="E43">A30</font></span></a>, <a class="txt" href="#E26:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E57">A48</font></span></a>, <a class="ref" href="polynom1.html#T28" title="POLYNOM1:th.28">POLYNOM1:28</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="E3:26_1_5_1_3_2_1_1_2_1_1_2_1_1_1"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="lab"><font color="Green" title="E48">A49</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)</span><br/><div class="add"><a NAME="E2:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:26_1"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E40:26_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></span>;<br/><a NAME="E3:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>;<br/><a NAME="E4:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<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="ref" href="polynom1.html#T15" title="POLYNOM1:th.15">POLYNOM1:15</a></span>;<br/><a NAME="E5:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<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="polynom1.html#T17" title="POLYNOM1:th.17">POLYNOM1:17</a></span>;<br/><a NAME="E6:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A50</font></span>: 
<font color="Maroon" title="c12">f</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</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="rlvect_1.html#T6" title="RLVECT_1:th.6">RLVECT_1:6</a></span>;<br/><a NAME="E7:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:26_1"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E27:26_1"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></span>;<br/><a NAME="E8:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K5" title="POLYNOM1:func.5">+</a> <span class="p2">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D6" title="POLYNOM1:def.6">POLYNOM1:def 6</a></span>;<br/><a NAME="E9:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<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="ref" href="polynom1.html#T15" title="POLYNOM1:th.15">POLYNOM1:15</a></span>;<br/><a NAME="E10:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<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="polynom1.html#T17" title="POLYNOM1:th.17">POLYNOM1:17</a></span>;<br/><a NAME="E11:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A51</font></span>: 
<font color="Maroon" title="c12">f</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="rlvect_1.html#T6" title="RLVECT_1:th.6">RLVECT_1:6</a></span>;<br/> <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</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="c12">f</font> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E50">A51</font></span></a>, <a class="ref" href="rlvect_1.html#T17" title="RLVECT_1:th.17">RLVECT_1:17</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span> <a href="polynom1.html#K3" title="POLYNOM1:func.3">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E48">A49</font></span></a>, <a class="txt" href="#E6:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E49">A50</font></span></a>, <a class="ref" href="rlvect_1.html#T17" title="RLVECT_1:th.17">RLVECT_1:17</a></span>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</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/><span class="kw">then </span> <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c19">m1</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c18">g1</font></span>)</span>,<font color="Maroon" title="c2">T</font>) = 
 <a href="polynom7.html#K1" title="POLYNOM7:func.1">Monom</a> (<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E48">A49</font></span></a>, <a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></span>
<br/>.= 
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c22">m2</font> <a href="polynom1.html#K10" title="POLYNOM1:func.10">*'</a> <font color="Maroon" title="c21">g2</font></span>)</span>,<font color="Maroon" title="c2">T</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></span>
;<br/><span class="kw">hence </span><a NAME="E14:26_1_5_1_3_2_1_1_2_1_1_2_1_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E14:26_1"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E33:26_1"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E9:26_1_5_1_3"><span class="lab"><font color="Green" title="E43">A30</font></span></a>, <a class="txt" href="#E1:26_1_5_1_3_2_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E47">A33</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="E3:26_1_5_1_3_2_1_1_2_1_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="E3:26_1_5_1_3_2_1_1_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="E2:26_1_5_1_3_2"/>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c17">f2</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">-</a> <font color="Maroon" title="c13">f1</font>, <a href="polynom1.html#K7" title="POLYNOM1:func.7">0_</a> (<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E13:26_1_5_1_3"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:26_1"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E23:26_1"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="ref" href="polyred.html#T50" title="POLYRED:th.50">POLYRED:50</a>, <a class="ref" href="rewrite1.html#T40" title="REWRITE1:th.40">REWRITE1:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="E44:26_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a>  <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E4:26"/><span class="kw">then </span>
 <a href="polyred.html#K3" title="POLYRED:func.3">PolyRedRel</a> (<font color="Maroon" title="c4">P</font>,<font color="Maroon" title="c2">T</font>) is  <a href="rewrite1.html#V9" title="REWRITE1:attr.9">locally-confluent</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#D24" title="REWRITE1:def.24">REWRITE1:def 24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:26"/>
<font color="Maroon" title="c4">P</font> <a href="groeb_1.html#R1" title="GROEB_1:pred.1">is_Groebner_basis_wrt</a> <font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_1.html#D3" title="GROEB_1:def.3">GROEB_1:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
