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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">b</font> being   <a href="pre_poly.html#NM2" title="PRE_POLY:NM.2">bag</a> of <font color="Maroon" title="c1">n</font><br/>  for <font color="Olive" title="b2">s</font> being   <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/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</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>   st <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">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="Olive" title="b1">b</font></span>)</span>)</span>)</span> &amp; <font color="Olive" title="b4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">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"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Olive" title="b2">s</font></span>)</span>)</span>)</span> holds <br/> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Olive" title="b3">f</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="Olive" title="b4">g</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">s</font> being   <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/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</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>   st <font color="Olive" title="b2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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="c2">b</font></span>)</span>)</span>)</span> &amp; <font color="Olive" title="b3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Olive" title="b1">s</font></span>)</span>)</span>)</span> holds <br/> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Olive" title="b2">f</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="Olive" title="b3">g</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be   <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>; <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">f</font>, <font color="Olive" title="b2">g</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>   st <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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="c2">b</font></span>)</span>)</span>)</span> &amp; <font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>)</span>)</span> holds <br/> <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Olive" title="b1">f</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="Olive" title="b2">g</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be    <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> ; <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="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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="c2">b</font></span>)</span>)</span>)</span> &amp; <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>)</span>)</span> implies  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c4">f</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">g</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:20"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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="c2">b</font></span>)</span>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E2:20"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">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"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>)</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">  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c4">f</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">g</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">sb</font> =  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">sbs</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">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">sbs9b</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">xsb</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>,<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c10">xsbs</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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c11">xsbs9b</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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>);<br/>
<span class="kw">set </span><font color="Maroon" title="c12">xs</font> = <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">b</font></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">h</font> = <font color="Maroon" title="c2">b</font> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</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> <font color="Maroon" title="c2">b</font></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span></span>)</span>;<br/>
<a NAME="E3:20"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">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/>
<a NAME="E4:20"/><span class="lab"><font color="Green" title="E15">A4</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="E5:20"/><span class="lab"><font color="Green" title="E16">A5</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/>
<a NAME="E6:20"/><span class="lab"><font color="Green" title="E17">A6</font></span>: 
 <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="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="ref" href="orders_1.html#T19" onmouseover="rs('orders_1/T19')" onmouseout="rh()">ORDERS_1:19</a>, <a class="ref" href="orders_1.html#T37" onmouseover="rs('orders_1/T37')" onmouseout="rh()">ORDERS_1:37</a></span>;<br/>
<a NAME="E7:20"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
 <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> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E16">A5</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="E8:20"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
 <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>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E16">A5</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="E9:20"/><span class="lab"><font color="Green" title="E20">A9</font></span>: 
 <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E16">A5</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="E10:20"/><span class="lab"><font color="Green" title="E21">A10</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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.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="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="ref" href="pre_poly.html#D2" onmouseover="rs('pre_poly/D2')" onmouseout="rh()">PRE_POLY:def 2</a></span>;<br/>
<a NAME="E11:20"/><span class="lab"><font color="Green" title="E22">A11</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>,<span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="pre_poly.html#D2" onmouseover="rs('pre_poly/D2')" onmouseout="rh()">PRE_POLY:def 2</a></span>;<br/>
<a NAME="E12:20"/><span class="lab"><font color="Green" title="E23">A12</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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:20"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="pre_poly.html#D2" onmouseover="rs('pre_poly/D2')" onmouseout="rh()">PRE_POLY:def 2</a></span>;<br/>
<a NAME="E13:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A13</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</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> <font color="Maroon" title="c2">b</font></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:20"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="ref" href="finseq_1.html#T31" onmouseover="rs('finseq_1/T31')" onmouseout="rh()">FINSEQ_1:31</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c14">h</font> = <font color="Maroon" title="c2">b</font> <a href="pre_poly.html#K23" title="PRE_POLY:func.23">*</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> <font color="Maroon" title="c2">b</font></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span></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="#E3:20"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="finseq_1.html#T16" onmouseover="rs('finseq_1/T16')" onmouseout="rh()">FINSEQ_1:16</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:20_1"/>
( <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c1">n</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>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1"><span class="kw">suppose </span></a><a NAME="E1:20_1_1"/>
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c4">f</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">g</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:20_1_1"/>
 <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c4">f</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">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E13">A2</font></span></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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2"><span class="kw">suppose </span></a><a NAME="E1:20_1_2"/>
<font color="Maroon" title="c1">n</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> 
 ; <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="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c4">f</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">g</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">n</font> = <font color="Maroon" title="c1">n</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">Ordinal</a> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c16">xsb</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>,<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span>), <font color="Maroon" title="c17">xsbs9b</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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>) as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c15">n</font> ;<br/><a NAME="E4:20_1_2"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c18">b</font> = <font color="Maroon" title="c2">b</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c15">n</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="funct_2.html#T2" onmouseover="rs('funct_2/T2')" onmouseout="rh()">FUNCT_2:2</a></span>;<br/><a NAME="E6:20_1_2"/>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c14">h</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="c18">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="E7:20_1_2"/><span class="kw">then </span>
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c14">h</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="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="c19">h</font> = <font color="Maroon" title="c14">h</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_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="c20">gr</font> = <font color="Maroon" title="c5">g</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/><a NAME="E10:20_1_2"/><span class="lab"><font color="Green" title="E25">A14</font></span>: 
 <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T79" onmouseover="rs('xboole_1/T79')" onmouseout="rh()">XBOOLE_1:79</a></span>;<br/><span class="lab"><font color="Green" title="E26">A15</font></span>: <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font>

<br/>.= 
<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T4" onmouseover="rs('xboole_1/T4')" onmouseout="rh()">XBOOLE_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T39" onmouseover="rs('xboole_1/T39')" onmouseout="rh()">XBOOLE_1:39</a></span>
;<br/> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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> <font color="Maroon" title="c2">b</font></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c16">xsb</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T22" onmouseover="rs('finseq_1/T22')" onmouseout="rh()">FINSEQ_1:22</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="orders_1.html#T38" onmouseover="rs('orders_1/T38')" onmouseout="rh()">ORDERS_1:38</a>, <a class="ref" href="pre_poly.html#T11" onmouseover="rs('pre_poly/T11')" onmouseout="rh()">PRE_POLY:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="orders_1.html#T38" onmouseover="rs('orders_1/T38')" onmouseout="rh()">ORDERS_1:38</a>, <a class="ref" href="pre_poly.html#T11" onmouseover="rs('pre_poly/T11')" onmouseout="rh()">PRE_POLY:11</a></span>
<br/>.= 
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:20_1_2"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="ref" href="card_2.html#T40" onmouseover="rs('card_2/T40')" onmouseout="rh()">CARD_2:40</a>, <a class="ref" href="xboole_1.html#T79" onmouseover="rs('xboole_1/T79')" onmouseout="rh()">XBOOLE_1:79</a></span>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="orders_1.html#T38" onmouseover="rs('orders_1/T38')" onmouseout="rh()">ORDERS_1:38</a>, <a class="ref" href="pre_poly.html#T11" onmouseover="rs('pre_poly/T11')" onmouseout="rh()">PRE_POLY:11</a></span>
;<br/><a NAME="E13:20_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A16</font></span>: 
 <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>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>)</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"><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> <font color="Maroon" title="c2">b</font></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T29" onmouseover="rs('finseq_3/T29')" onmouseout="rh()">FINSEQ_3:29</a></span>;<br/><a NAME="E14:20_1_2"/><span class="lab"><font color="Green" title="E28">A17</font></span>: 
 <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>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span>) is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="orders_1.html#T38" onmouseover="rs('orders_1/T38')" onmouseout="rh()">ORDERS_1:38</a>, <a class="ref" href="pre_poly.html#T10" onmouseover="rs('pre_poly/T10')" onmouseout="rh()">PRE_POLY:10</a></span>;<br/><a NAME="E15:20_1_2"/><span class="lab"><font color="Green" title="E29">A18</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c16">xsb</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="ref" href="pre_poly.html#D2" onmouseover="rs('pre_poly/D2')" onmouseout="rh()">PRE_POLY:def 2</a></span>;<br/><a NAME="E16:20_1_2"/><span class="lab"><font color="Green" title="E30">A19</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c17">xsbs9b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:20"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="pre_poly.html#D2" onmouseover="rs('pre_poly/D2')" onmouseout="rh()">PRE_POLY:def 2</a></span>;<br/><a NAME="E17:20_1_2"/><span class="lab"><font color="Green" title="E31">A20</font></span>: 
<font color="Maroon" title="c16">xsb</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="orders_1.html#T38" onmouseover="rs('orders_1/T38')" onmouseout="rh()">ORDERS_1:38</a>, <a class="ref" href="pre_poly.html#T10" onmouseover="rs('pre_poly/T10')" onmouseout="rh()">PRE_POLY:10</a></span>;<br/><a NAME="E18:20_1_2"/>
<font color="Maroon" title="c17">xsbs9b</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="orders_1.html#T38" onmouseover="rs('orders_1/T38')" onmouseout="rh()">ORDERS_1:38</a>, <a class="ref" href="pre_poly.html#T10" onmouseover="rs('pre_poly/T10')" onmouseout="rh()">PRE_POLY:10</a></span>;<br/><a NAME="E19:20_1_2"/><span class="kw">then </span>
<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">b</font></span>)</span>)</span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="finsub_1.html#K1" title="FINSUB_1:func.1">\/</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="finsub_1.html#K2" title="FINSUB_1:func.2">\</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span>)</span>)</span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:20_1_2"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E15:20_1_2"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="txt" href="#E16:20_1_2"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E17:20_1_2"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="ref" href="finseq_3.html#T91" onmouseover="rs('finseq_3/T91')" onmouseout="rh()">FINSEQ_3:91</a></span>;<br/><a NAME="E20:20_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A21</font></span>: 
<font color="Maroon" title="c20">gr</font>,<font color="Maroon" title="c19">h</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E11:20_1_2"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E13:20_1_2"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E14:20_1_2"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="classes1.html#T83" onmouseover="rs('classes1/T83')" onmouseout="rh()">CLASSES1:83</a>, <a class="ref" href="rfinseq.html#T26" onmouseover="rs('rfinseq/T26')" onmouseout="rh()">RFINSEQ:26</a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="20_1_2_3"><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#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> <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="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> &amp; (  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> ) )</span></a><div class="add"><span class="kw">thus </span><a NAME="E1:20_1_2_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> <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="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E12:20"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="relat_1.html#T27" onmouseover="rs('relat_1/T27')" onmouseout="rh()">RELAT_1:27</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#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> &amp; (  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> ) )</span><br/><a NAME="E2:20_1_2_3"/><span class="lab"><font color="Green" title="E33">A22</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c17">xsbs9b</font></span>)</span>
 <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/><span class="kw">hence </span><a NAME="E3:20_1_2_3"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" onmouseover="rs('funcop_1/T13')" onmouseout="rh()">FUNCOP_1:13</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">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span><br/><span class="kw">let </span><font color="Maroon" title="c21">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font> )</span><br/><span class="kw">assume </span><a NAME="E4:20_1_2_3"/><span class="lab"><font color="Green" title="E34">A23</font></span>: 
<font color="Maroon" title="c21">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c17">xsbs9b</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font></span><br/><a NAME="E5:20_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c17">xsbs9b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c17">xsbs9b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/><a NAME="E6:20_1_2_3"/><span class="kw">then </span>
 not <font color="Maroon" title="c17">xsbs9b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <font color="Maroon" title="c2">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:20"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="ref" href="xboole_0.html#D5" onmouseover="rs('xboole_0/D5')" onmouseout="rh()">XBOOLE_0:def 5</a></span>;<br/><a NAME="E7:20_1_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c18">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">xsbs9b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#D7" onmouseover="rs('pre_poly/D7')" onmouseout="rh()">PRE_POLY:def 7</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font> = 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20_1_2_3"><span class="lab"><font color="Green" title="E34">A23</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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K5" title="FINSEQ_2:func.5">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c21">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20_1_2_3"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="txt" href="#E4:20_1_2_3"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="ref" href="funcop_1.html#T7" onmouseover="rs('funcop_1/T7')" onmouseout="rh()">FUNCOP_1:7</a></span>
;<br/> <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="E22:20_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A24</font></span>: 
<font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span> <a href="finseq_2.html#K2" title="FINSEQ_2:func.2">|-&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T2" onmouseover="rs('funct_1/T2')" onmouseout="rh()">FUNCT_1:2</a></span>;<br/><a NAME="E23:20_1_2"/>
<font color="Maroon" title="c19">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c16">xsb</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseqop.html#T9" onmouseover="rs('finseqop/T9')" onmouseout="rh()">FINSEQOP:9</a></span>;<br/><span class="kw">then </span> <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <font color="Maroon" title="c19">h</font> = 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c16">xsb</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c18">b</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Maroon" title="c17">xsbs9b</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T75" onmouseover="rs('rvsum_1/T75')" onmouseout="rh()">RVSUM_1:75</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E22:20_1_2"><span class="lab"><font color="Green" title="E33">A24</font></span></a>, <a class="ref" href="rvsum_1.html#T81" onmouseover="rs('rvsum_1/T81')" onmouseout="rh()">RVSUM_1:81</a></span>
;<br/><span class="kw">hence </span><a NAME="E25:20_1_2"/>
 <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <font color="Maroon" title="c4">f</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">g</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:20_1_2"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="ref" href="rfinseq.html#T9" onmouseover="rs('rfinseq/T9')" onmouseout="rh()">RFINSEQ:9</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></div><span class="kw">end;</span></div>

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