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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font> holds   <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Olive" title="b2">b</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c3">b</font></span>)</span></span><br/>



<a NAME="E1:21"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">field</a> <span class="p1">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="wellord2.html#D1" onmouseover="rs('wellord2/D1')" onmouseout="rh()">WELLORD2:def 1</a></span>;<br/>
<a NAME="E2:21"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
 <a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font> is  <a href="orders_1.html#V3" title="ORDERS_1:attr.3">being_linear-order</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_1.html#T19" onmouseover="rs('orders_1/T19')" onmouseout="rh()">ORDERS_1:19</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">fab</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw"> such that </span><br/><a NAME="E4:21"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c4">fab</font>
 <span class="kw">and </span><br/><a NAME="E5:21"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c4">fab</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bagorder.html#D4" target="_self" onmouseover="rs('bagorder/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">fa</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw"> such that </span><br/><a NAME="E7:21"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c5">fa</font>
 <span class="kw">and </span><br/><a NAME="E8:21"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
<font color="Maroon" title="c5">fa</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">a</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bagorder.html#D4" target="_self" onmouseover="rs('bagorder/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">fb</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <span class="kw"> such that </span><br/><a NAME="E10:21"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c6">fb</font>
 <span class="kw">and </span><br/><a NAME="E11:21"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<font color="Maroon" title="c6">fb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c3">b</font></span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="bagorder.html#D4" target="_self" onmouseover="rs('bagorder/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">fab9</font> = <font color="Maroon" title="c4">fab</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T24" onmouseover="rs('finseq_2/T24')" onmouseout="rh()">FINSEQ_2:24</a>, <a class="ref" href="numbers.html#T19" onmouseover="rs('numbers/T19')" onmouseout="rh()">NUMBERS:19</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">sasb</font> = <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c3">b</font></span>)</span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">sasb</font> = <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c3">b</font></span>)</span> as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">n</font> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">s</font> =  <a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p1">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c9">sasb</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c11">fa9b</font> = <font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c9">sasb</font>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">fb9a</font> = <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c9">sasb</font>)</span>)</span>;<br/>
<a NAME="E14:21"/>
 <a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font> <a href="orders_1.html#R3" title="ORDERS_1:pred.3">linearly_orders</a> <font color="Maroon" title="c9">sasb</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="orders_1.html#T37" onmouseover="rs('orders_1/T37')" onmouseout="rh()">ORDERS_1:37</a>, <a class="ref" href="orders_1.html#T38" onmouseover="rs('orders_1/T38')" onmouseout="rh()">ORDERS_1:38</a></span>;<br/>
<a NAME="E15:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A9</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c9">sasb</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">sasb</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D2" onmouseover="rs('pre_poly/D2')" onmouseout="rh()">PRE_POLY:def 2</a></span>;<br/>
<a NAME="E16:21"/><span class="lab"><font color="Green" title="E22">A10</font></span>: 
 <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">sasb</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T38" onmouseover="rs('pre_poly/T38')" onmouseout="rh()">PRE_POLY:38</a></span>;<br/>
<a NAME="E17:21"/><span class="lab"><font color="Green" title="E23">A11</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E18:21"/><span class="lab"><font color="Green" title="E24">A12</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">fa9b</font> = <font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c9">sasb</font>)</span>)</span>, <font color="Maroon" title="c14">fb9a</font> = <font color="Maroon" title="c3">b</font> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c9">sasb</font>)</span>)</span> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:21"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E17:21"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="finseq_1.html#T16" onmouseover="rs('finseq_1/T16')" onmouseout="rh()">FINSEQ_1:16</a></span>;<br/>
<a NAME="E20:21"/><span class="lab"><font color="Green" title="E25">A13</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c13">fa9b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T26" onmouseover="rs('relat_1/T26')" onmouseout="rh()">RELAT_1:26</a></span>;<br/>
<a NAME="E21:21"/><span class="lab"><font color="Green" title="E26">A14</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c14">fb9a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T26" onmouseover="rs('relat_1/T26')" onmouseout="rh()">RELAT_1:26</a></span>;<br/>
<a NAME="E22:21"/><span class="lab"><font color="Green" title="E27">A15</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c13">fa9b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_0.html#D6" onmouseover="rs('valued_0/D6')" onmouseout="rh()">VALUED_0:def 6</a></span>;<br/>
<a NAME="E23:21"/><span class="lab"><font color="Green" title="E28">A16</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c14">fb9a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_0.html#D6" onmouseover="rs('valued_0/D6')" onmouseout="rh()">VALUED_0:def 6</a></span>;<br/>
<a NAME="E24:21"/><span class="lab"><font color="Green" title="E29">A17</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c13">fa9b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:21"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<a NAME="E25:21"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c14">fb9a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:21"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">fa9b</font> = <font color="Maroon" title="c13">fa9b</font>, <font color="Maroon" title="c16">fb9a</font> = <font color="Maroon" title="c14">fb9a</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:21"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">fa9bn</font> = <font color="Maroon" title="c15">fa9b</font>, <font color="Maroon" title="c18">fb9an</font> = <font color="Maroon" title="c16">fb9a</font> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:21"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E23:21"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="ref" href="finseq_1.html#D4" onmouseover="rs('finseq_1/D4')" onmouseout="rh()">FINSEQ_1:def 4</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">ln</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font>;<br/>
<a NAME="E28:21"/><span class="lab"><font color="Green" title="E30">A18</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>;<br/>
<span class="lab"><font color="Green" title="E31">A19</font></span>:  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">fab</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>
<br/>.= 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p2">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<font color="Maroon" title="c9">sasb</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E15:21"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E16:21"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E28:21"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="ref" href="relat_1.html#T27" onmouseover="rs('relat_1/T27')" onmouseout="rh()">RELAT_1:27</a></span>
;<br/>
<a NAME="E30:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A20</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c15">fa9b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:21"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E17:21"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="relat_1.html#T27" onmouseover="rs('relat_1/T27')" onmouseout="rh()">RELAT_1:27</a></span>;<br/>
<a NAME="E31:21"/><span class="lab"><font color="Green" title="E33">A21</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c16">fb9a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:21"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E18:21"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E29:21"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="ref" href="relat_1.html#T27" onmouseover="rs('relat_1/T27')" onmouseout="rh()">RELAT_1:27</a></span>;<br/>
<a NAME="E32:21"/><span class="lab"><font color="Green" title="E34">A22</font></span>: 
 <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c5">fa</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c17">fa9bn</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:21"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="bagorder.html#T12" target="_self" onmouseover="rs('bagorder/T12')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E33:21"/><span class="lab"><font color="Green" title="E35">A23</font></span>: 
 <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c6">fb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c18">fb9an</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:21"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="bagorder.html#T12" target="_self" onmouseover="rs('bagorder/T12')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E34:21"/><span class="lab"><font color="Green" title="E36">A24</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">fa9b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c16">fb9a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:21"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="txt" href="#E31:21"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/>
<a NAME="E35:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A25</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">fa9b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="integra5.html#T2" onmouseover="rs('integra5/T2')" onmouseout="rh()">INTEGRA5:2</a></span>;<br/>
<a NAME="E36:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A26</font></span>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:21"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">fa9b9</font> = <font color="Maroon" title="c15">fa9b</font> as   <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:21"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a>, <a class="ref" href="relat_1.html#D18" onmouseover="rs('relat_1/D18')" onmouseout="rh()">RELAT_1:def 18</a></span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="21_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">fab9</font> &amp;  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> &amp; (  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> holds <br/><font color="Maroon" title="c7">fab9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> ) )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:21_2"/>
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">fab9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" onmouseover="rs('finseq_1/D3')" onmouseout="rh()">FINSEQ_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> &amp; (  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> holds <br/><font color="Maroon" title="c7">fab9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> ) )</span><br/><span class="kw">thus </span><a NAME="E2:21_2"/>
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:21"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="txt" href="#E35:21"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> holds <br/><font color="Maroon" title="c7">fab9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c21">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span> implies <font color="Maroon" title="c7">fab9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font> )</span><br/><span class="kw">assume </span><a NAME="E3:21_2"/><span class="lab"><font color="Green" title="E39">A27</font></span>: 
<font color="Maroon" title="c21">k</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">fab</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">fab9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c22">k1</font> = <font color="Maroon" title="c21">k</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c23">fa9bk</font> = <font color="Maroon" title="c15">fa9b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">k1</font>, <font color="Maroon" title="c24">fb9ak</font> = <font color="Maroon" title="c16">fb9a</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c22">k1</font> as   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ;<br/><span class="kw">thus </span><font color="Maroon" title="c7">fab9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p3">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E16:21"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E29:21"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="txt" href="#E3:21_2"><span class="lab"><font color="Green" title="E39">A27</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p4">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p4">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D5" onmouseover="rs('pre_poly/D5')" onmouseout="rh()">PRE_POLY:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c20">fa9b9</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c21">k</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">b</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K7" title="PRE_POLY:func.7">SgmX</a> (<span class="p4">(<span class="default"><a href="orders_1.html#K2" title="ORDERS_1:func.2">RelIncl</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span></span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:21"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E29:21"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="txt" href="#E3:21_2"><span class="lab"><font color="Green" title="E39">A27</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c23">fa9bk</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c24">fb9ak</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:21"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E29:21"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="txt" href="#E3:21_2"><span class="lab"><font color="Green" title="E39">A27</font></span></a>, <a class="ref" href="funct_1.html#T13" onmouseover="rs('funct_1/T13')" onmouseout="rh()">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:21"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="txt" href="#E3:21_2"><span class="lab"><font color="Green" title="E39">A27</font></span></a>, <a class="ref" href="valued_1.html#D1" onmouseover="rs('valued_1/D1')" onmouseout="rh()">VALUED_1:def 1</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E39:21"/><span class="kw">then </span>
<font color="Maroon" title="c7">fab9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">fa9b</font> <a href="rvsum_1.html#K4" title="RVSUM_1:func.4">+</a> <font color="Maroon" title="c16">fb9a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T13" onmouseover="rs('finseq_1/T13')" onmouseout="rh()">FINSEQ_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E40:21"/>
 <a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="pre_poly.html#K11" title="PRE_POLY:func.11">+</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="bagorder.html#K3" title="BAGORDER:func.3">TotDegree</a> <font color="Maroon" title="c3">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:21"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E7:21"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E10:21"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E32:21"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="txt" href="#E33:21"><span class="lab"><font color="Green" title="E35">A23</font></span></a>, <a class="txt" href="#E34:21"><span class="lab"><font color="Green" title="E36">A24</font></span></a>, <a class="ref" href="integra5.html#T2" onmouseover="rs('integra5/T2')" onmouseout="rh()">INTEGRA5:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
