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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T</font> being  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>   <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font><br/> for <font color="Olive" title="b2">L</font> being non  <a href="struct_0.html#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">I</font> being  <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>   <a href="ideal_1.html#V2" title="IDEAL_1:attr.2">left-ideal</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font></span>)</span><br/> for <font color="Olive" title="b4">m</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><br/> for <font color="Olive" title="b5">f</font>, <font color="Olive" title="b6">g</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="b5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">I</font> &amp; <font color="Olive" title="b6">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">I</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b5">f</font>,<font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">m</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b6">g</font>,<font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">m</font> &amp; ( for <font color="Olive" title="b7">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>  holds <br/>(  not <font color="Olive" title="b7">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">I</font> or  not <font color="Olive" title="b7">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b5">f</font>,<font color="Olive" title="b1">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b7">p</font>,<font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">m</font> ) ) &amp; ( for <font color="Olive" title="b7">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b2">L</font>  holds <br/>(  not <font color="Olive" title="b7">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">I</font> or  not <font color="Olive" title="b7">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b6">g</font>,<font color="Olive" title="b1">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b7">p</font>,<font color="Olive" title="b1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">m</font> ) ) holds <br/><font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">g</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">T</font> be   <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>   <a href="bagorder.html#V2" title="BAGORDER:attr.2">admissible</a>  <a href="bagorder.html#NM1" title="BAGORDER:NM.1">TermOrder</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">L</font> being non  <a href="struct_0.html#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">I</font> being  <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>   <a href="ideal_1.html#V2" title="IDEAL_1:attr.2">left-ideal</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font></span>)</span><br/> for <font color="Olive" title="b3">m</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><br/> for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</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="b4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">I</font> &amp; <font color="Olive" title="b5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">I</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b4">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b5">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> &amp; ( for <font color="Olive" title="b6">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>  holds <br/>(  not <font color="Olive" title="b6">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">I</font> or  not <font color="Olive" title="b6">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b4">f</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b6">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> ) ) &amp; ( for <font color="Olive" title="b6">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">L</font>  holds <br/>(  not <font color="Olive" title="b6">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">I</font> or  not <font color="Olive" title="b6">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b5">g</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b6">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> ) ) holds <br/><font color="Olive" title="b4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">g</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>   <a href="ideal_1.html#V2" title="IDEAL_1:attr.2">left-ideal</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span><br/> for <font color="Olive" title="b2">m</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><br/> for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</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="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">I</font> &amp; <font color="Olive" title="b4">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">I</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b3">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">m</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b4">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">m</font> &amp; ( for <font color="Olive" title="b5">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">I</font> or  not <font color="Olive" title="b5">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b3">f</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b5">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">m</font> ) ) &amp; ( for <font color="Olive" title="b5">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">I</font> or  not <font color="Olive" title="b5">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b4">g</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b5">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">m</font> ) ) holds <br/><font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">g</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">I</font> be   <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>   <a href="ideal_1.html#V2" title="IDEAL_1:attr.2">left-ideal</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">m</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><br/> for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</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">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp; <font color="Olive" title="b3">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b2">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b3">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> &amp; ( for <font color="Olive" title="b4">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b2">f</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b4">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> ) ) &amp; ( for <font color="Olive" title="b4">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b4">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b3">g</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b4">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> ) ) holds <br/><font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">g</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">m</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</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">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp; <font color="Olive" title="b2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b2">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> &amp; ( for <font color="Olive" title="b3">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b3">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b3">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> ) ) &amp; ( for <font color="Olive" title="b3">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b3">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Olive" title="b2">g</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b3">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> ) ) holds <br/><font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">g</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">f</font>, <font color="Maroon" title="c7">g</font> be   <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp; <font color="Maroon" title="c7">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> &amp; ( for <font color="Olive" title="b1">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> ) ) &amp; ( for <font color="Olive" title="b1">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> ) ) implies <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:53"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font>
 <span class="kw">and </span><br/><a NAME="E2:53"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<font color="Maroon" title="c7">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font>
 <span class="kw">and </span><br/><a NAME="E3:53"/><span class="lab"><font color="Green" title="E40">A3</font></span>: 
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font>
 <span class="kw">and </span><br/><a NAME="E4:53"/><span class="lab"><font color="Green" title="E41">A4</font></span>: 
 <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">p</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 <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp; <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> ) or  ex <font color="Olive" title="b1">p</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 <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> &amp; <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> ) or <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font> )</span><br/>

<span class="lab"><font color="Green" title="E42">A5</font></span>:  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> = 
 <a href="polynom7.html#K2" title="POLYNOM7:func.2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T22" title="TERMORD:th.22">TERMORD:22</a></span>
<br/>.= 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:53"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="txt" href="#E4:53"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="termord.html#T22" title="TERMORD:th.22">TERMORD:22</a></span>
;<br/>
<span class="lab"><font color="Green" title="E43">A6</font></span>:  <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> = 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<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/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#T18" title="TERMORD:th.18">TERMORD:18</a></span>
<br/>.= 
<font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:53"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="txt" href="#E4:53"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="#E5:53"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="ref" href="termord.html#T18" title="TERMORD:th.18">TERMORD:18</a></span>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c7">g</font>,<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">assume </span><span class="kw">that </span><br/><a NAME="E7:53"/><span class="lab"><font color="Green" title="E44">A7</font></span>: 
for <font color="Olive" title="b1">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> )
 <span class="kw">and </span><br/><a NAME="E8:53"/><span class="lab"><font color="Green" title="E45">A8</font></span>: 
for <font color="Olive" title="b1">p</font> being  <a href="polynom1.html#NM2" title="POLYNOM1:NM.2">Polynomial</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>  holds <br/>(  not <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">I</font> or  not <font color="Olive" title="b1">p</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> or  not  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">m</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c8">I</font> = <font color="Maroon" title="c4">I</font> as   <a href="ideal_1.html#NM3" title="IDEAL_1:NM.3">LeftIdeal</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K13" title="POLYNOM1:func.13">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="txt" href="#E1:53"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3"><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="E1:53_3"/>
( <font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or <font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3_1"><span class="kw">suppose </span></a><a NAME="E1:53_3_1"/>
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font></span><br/><div class="add"><span class="kw">hence </span><font color="Maroon" title="c7">g</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <font color="Maroon" title="c7">g</font>
<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="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <font color="Maroon" title="c7">g</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <font color="Maroon" title="c7">g</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T80" title="POLYNOM1:th.80">POLYNOM1:80</a></span>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p1">(<span class="default"><a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T3" title="POLYRED:th.3">POLYRED:3</a></span>
<br/>.= 
<font color="Maroon" title="c6">f</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T82" title="POLYNOM1:th.82">POLYNOM1:82</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3_2"><span class="kw">suppose </span></a><a NAME="E1:53_3_2"/><span class="lab"><font color="Green" title="E46">A9</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_3_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_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="E1:53_3_2_1_1"/>
( <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> or ( <font color="Maroon" title="c6">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c7">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3_2_1_1_1"><span class="kw">case </span></a><a NAME="E1:53_3_2_1_1_1"/><span class="lab"><font color="Green" title="E47">A10</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font></span><br/><div class="add"><a NAME="E2:53_3_2_1_1_1"/><span class="kw">then </span>
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font> <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="#E6:53"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>;<br/><span class="kw">hence </span><a NAME="E3:53_3_2_1_1_1"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53_3_2_1_1_1"><span class="lab"><font color="Green" title="E47">A10</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3_2_1_1_2"><span class="kw">case </span></a><a NAME="E1:53_3_2_1_1_2"/><span class="lab"><font color="Green" title="E47">A11</font></span>: 
<font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font></span><br/><div class="add"><a NAME="E2:53_3_2_1_1_2"/><span class="kw">then </span>
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <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="#E6:53"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>;<br/><span class="kw">hence </span><a NAME="E3:53_3_2_1_1_2"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53_3_2_1_1_2"><span class="lab"><font color="Green" title="E47">A11</font></span></a>, <a class="ref" href="termord.html#T17" title="TERMORD:th.17">TERMORD:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="53_3_2_1_1_3"><span class="kw">case </span></a><a NAME="E1:53_3_2_1_1_3"/><span class="lab"><font color="Green" title="E47">A12</font></span>: 
( <font color="Maroon" title="c6">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c7">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c9">s</font> =  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font>;<br/><span class="kw">set </span><font color="Maroon" title="c10">d</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c11">c</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c12">h</font> = <font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>;<br/><a NAME="E2:53_3_2_1_1_3"/><span class="lab"><font color="Green" title="E48">A13</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53_3_2"><span class="lab"><font color="Green" title="E46">A9</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E3:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A14</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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/><div><span class="lab"><font color="Green" title="E50">A15</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="53_3_2_1_1_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:53_3_2_1_1_3_1"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:53"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<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"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1:def 22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></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"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:53"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:53_3_2_1_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E49">A14</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E5:53_3_2_1_1_3"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="termord.html#R1" title="TERMORD:pred.1">&lt;=</a>  <a href="termord.html#K2" title="TERMORD:func.2">max</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:53"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="ref" href="groeb_1.html#T7" target="_self" title="GROEB_1:th.7">Th7</a></span>;<br/><a NAME="E6:53_3_2_1_1_3"/><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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="c6">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="ref" href="termord.html#T12" title="TERMORD:th.12">TERMORD:12</a></span>;<br/><a NAME="E7:53_3_2_1_1_3"/><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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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> <font color="Maroon" title="c6">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="#E4:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E50">A15</font></span></a>, <a class="ref" href="termord.html#D3" title="TERMORD:def.3">TERMORD:def 3</a></span>;<br/><a NAME="E8:53_3_2_1_1_3"/><span class="kw">then </span>
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="E9:53_3_2_1_1_3"/><span class="kw">then </span>
not  <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="E10:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A16</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<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#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><span class="lab"><font color="Green" title="E52">A17</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1:def 22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<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"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></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#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E51">A16</font></span></a>, <a class="ref" href="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T25" title="RLVECT_1:th.25">RLVECT_1:25</a></span>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></span>
;<br/><a NAME="E12:53_3_2_1_1_3"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E47">A12</font></span></a>, <a class="ref" href="polynom7.html#T1" title="POLYNOM7:th.1">POLYNOM7:1</a></span>;<br/><a NAME="E13:53_3_2_1_1_3"/><span class="kw">then </span>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E14:53_3_2_1_1_3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<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="#E11:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E52">A17</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><a NAME="E15:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A18</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><a NAME="E16:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A19</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E17:53_3_2_1_1_3"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>;<br/><a NAME="E18:53_3_2_1_1_3"/><span class="kw">then </span>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T79" title="POLYNOM1:th.79">POLYNOM1:79</a></span>;<br/><a NAME="E19:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A20</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_1.html#T5" target="_self" title="GROEB_1:th.5">Th5</a></span>;<br/><a NAME="E20:53_3_2_1_1_3"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T19" title="POLYRED:th.19">POLYRED:19</a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></span>;<br/><a NAME="E21:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A21</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E55">A20</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E22:53_3_2_1_1_3"/>
not <font color="Maroon" title="c7">g</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="txt" href="#E4:53"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="#E7:53"><span class="lab"><font color="Green" title="E44">A7</font></span></a></span>;<br/><a NAME="E23:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A22</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T29" title="POLYRED:th.29">POLYRED:29</a></span>;<br/><a NAME="E24:53_3_2_1_1_3"/>
not <font color="Maroon" title="c6">f</font> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E3:53"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="txt" href="#E8:53"><span class="lab"><font color="Green" title="E45">A8</font></span></a></span>;<br/><a NAME="E25:53_3_2_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">g</font> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polyred.html#T29" title="POLYRED:th.29">POLYRED:29</a></span>;<br/><a NAME="E26:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A23</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E57">A22</font></span></a>, <a class="ref" href="polyred.html#T26" title="POLYRED:th.26">POLYRED:26</a></span>;<br/><a NAME="E27:53_3_2_1_1_3"/>
(  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> &amp;  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#T79" title="POLYNOM1:th.79">POLYNOM1:79</a>, <a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>;<br/><a NAME="E28:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A24</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c7">g</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="groeb_1.html#T5" target="_self" title="GROEB_1:th.5">Th5</a></span>;<br/><a NAME="E29:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A25</font></span>: 
<span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E58">A23</font></span></a>, <a class="ref" href="xboole_1.html#T9" title="XBOOLE_1:th.9">XBOOLE_1:9</a></span>;<br/><a NAME="E30:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A26</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E56">A21</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E31:53_3_2_1_1_3"/>
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E53">A18</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E32:53_3_2_1_1_3"/><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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></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="c6">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="#E30:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E61">A26</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><a NAME="E33:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A27</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></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> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E54">A19</font></span></a>, <a class="ref" href="termord.html#T7" title="TERMORD:th.7">TERMORD:7</a></span>;<br/><span class="kw">then </span> <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c2">T</font> = 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E52">A17</font></span></a>, <a class="ref" href="termord.html#D7" title="TERMORD:def.7">TERMORD:def 7</a></span>
<br/>.= 
 <a href="termord.html#K4" title="TERMORD:func.4">HC</a> <font color="Maroon" title="c6">f</font>,<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><span class="lab"><font color="Green" title="E63">A28</font></span>:  <a href="termord.html#K5" title="TERMORD:func.5">HM</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></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> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>,<span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E62">A27</font></span></a>, <a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></span>
<br/>.= 
<font color="Maroon" title="c5">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:53"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="termord.html#D8" title="TERMORD:def.8">TERMORD:def 8</a></span>
;<br/><span class="kw">reconsider </span><font color="Maroon" title="c13">cp</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </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>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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#K13" title="POLYNOM1:func.13">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#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c14">cc</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </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> 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#K13" title="POLYNOM1:func.13">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#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c15">f9</font> = <font color="Maroon" title="c6">f</font>, <font color="Maroon" title="c16">g9</font> = <font color="Maroon" title="c7">g</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#K13" title="POLYNOM1:func.13">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#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></span>;<br/><span class="lab"><font color="Green" title="E64">A29</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D22" title="POLYNOM1:def.22">POLYNOM1:def 22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="rlvect_1.html#D14" title="RLVECT_1:def.14">RLVECT_1:def 14</a></span>
;<br/><a NAME="E40:53_3_2_1_1_3"/><span class="lab"><font color="Green" title="E65">A30</font></span>: 
 <a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E48">A13</font></span></a>, <a class="ref" href="termord.html#D6" title="TERMORD:def.6">TERMORD:def 6</a></span>;<br/><div><span class="lab"><font color="Green" title="E66">A31</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="53_3_2_1_1_3_6"><span class="kw">now </span></a><div class="add"><a NAME="E1:53_3_2_1_1_3_6"/><span class="lab"><font color="Green" title="E67">A32</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="#E40:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E65">A30</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>;<br/><span class="lab"><font color="Green" title="E68">A33</font></span>:  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span> = 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="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="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E64">A29</font></span></a>, <a class="txt" href="#E1:53_3_2_1_1_3_6"><span class="lab"><font color="Green" title="E67">A32</font></span></a>, <a class="ref" href="vectsp_1.html#D22" title="VECTSP_1:def.22">VECTSP_1:def 22</a></span>
<br/>.= 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="vectsp_1.html#D19" title="VECTSP_1:def.19">VECTSP_1:def 19</a></span>
;<br/><span class="kw">assume </span><a NAME="E3:53_3_2_1_1_3_6"/><span class="lab"><font color="Green" title="E69">A34</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c6">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K6" title="POLYNOM1:func.6">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D23" title="POLYNOM1:def.23">POLYNOM1:def 23</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D21" title="POLYNOM1:def.21">POLYNOM1:def 21</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="polyred.html#T9" title="POLYRED:th.9">POLYRED:9</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="polynom7.html#D10" title="POLYNOM7:def.10">POLYNOM7:def 10</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p2">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p3">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</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="txt" href="#E39:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E64">A29</font></span></a>, <a class="txt" href="#E2:53_3_2_1_1_3_6"><span class="lab"><font color="Green" title="E68">A33</font></span></a>, <a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">VECTSP_1:41</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c3">L</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:53_3_2_1_1_3_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E58">A23</font></span></a>, <a class="txt" href="#E3:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E49">A14</font></span></a>, <a class="txt" href="#E28:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E59">A24</font></span></a>, <a class="txt" href="#E3:53_3_2_1_1_3_6"><span class="lab"><font color="Green" title="E69">A34</font></span></a>, <a class="ref" href="polynom1.html#D9" title="POLYNOM1:def.9">POLYNOM1:def 9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E42:53_3_2_1_1_3"/>
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polyred.html#R1" title="POLYRED:pred.1">&lt;=</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E56">A21</font></span></a>, <a class="txt" href="#E29:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E60">A25</font></span></a>, <a class="ref" href="groeb_1.html#T8" target="_self" title="GROEB_1:th.8">Th8</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E43:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A35</font></span>: 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span> <a href="polyred.html#R2" title="POLYRED:pred.2">&lt;</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E66">A31</font></span></a>, <a class="ref" href="polyred.html#D3" title="POLYRED:def.3">POLYRED:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c17">cp</font> = <font color="Maroon" title="c13">cp</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#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c18">cc</font> = <font color="Maroon" title="c14">cc</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#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c19">f9</font> = <font color="Maroon" title="c15">f9</font>, <font color="Maroon" title="c20">g9</font> = <font color="Maroon" title="c16">g9</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#K13" title="POLYNOM1:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c3">L</font></span>)</span> ;<br/><a NAME="E47:53_3_2_1_1_3"/>
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">f9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">g9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="groeb_1.html#E4"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a></span>;<br/><a NAME="E48:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A36</font></span>: 
<font color="Maroon" title="c17">cp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">cc</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">f9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">g9</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D27" title="POLYNOM1:def.27">POLYNOM1:def 27</a></span>;<br/><a NAME="E49:53_3_2_1_1_3"/>
<font color="Maroon" title="c19">f9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">g9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">I</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E2:53"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="ideal_1.html#T15" title="IDEAL_1:th.15">IDEAL_1:15</a></span>;<br/><a NAME="E50:53_3_2_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A37</font></span>: 
<font color="Maroon" title="c18">cc</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">f9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c20">g9</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ideal_1.html#D2" title="IDEAL_1:def.2">IDEAL_1:def 2</a></span>;<br/><font color="Maroon" title="c19">f9</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c17">cp</font> = 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p5">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </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>)</span> <a href="polynom1.html#K12" title="POLYNOM1:func.12">*'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="groeb_1.html#E4"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</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="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<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"><span class="p5">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c7">g</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <span class="p0">(<span class="default"><a href="termord.html#K3" title="TERMORD:func.3">HT</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span>,<font color="Maroon" title="c2">T</font></span>)</span></span>)</span></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"><font color="Maroon" title="c6">f</font> <a href="polynom1.html#K8" title="POLYNOM1:func.8">-</a> <font color="Maroon" title="c7">g</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T27" title="POLYNOM7:th.27">POLYNOM7:27</a></span>
;<br/><span class="kw">hence </span><a NAME="E52:53_3_2_1_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:53"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E7:53"><span class="lab"><font color="Green" title="E44">A7</font></span></a>, <a class="txt" href="#E35:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E63">A28</font></span></a>, <a class="txt" href="#E43:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E67">A35</font></span></a>, <a class="txt" href="#E50:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E69">A37</font></span></a>, <a class="txt" href="#E48:53_3_2_1_1_3"><span class="lab"><font color="Green" title="E68">A36</font></span></a>, <a class="ref" href="ideal_1.html#T15" title="IDEAL_1:th.15">IDEAL_1:15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:53_3_2"/>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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