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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">b1</font>, <font color="Olive" title="b2">b2</font> being   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>   <a href="pre_poly.html#V2" title="PRE_POLY:attr.2">finite-support</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">X</font>  st  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Olive" title="b1">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Olive" title="b2">b2</font> holds <br/> <a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Olive" title="b2">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Olive" title="b1">b1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Olive" title="b2">b2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">b1</font>, <font color="Maroon" title="c3">b2</font> be   <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>   <a href="pre_poly.html#V2" title="PRE_POLY:attr.2">finite-support</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">X</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="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c2">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c3">b2</font> implies  <a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Maroon" title="c2">b1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Maroon" title="c3">b2</font></span>)</span> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">b0</font> = <font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font>;<br/>
<span class="kw">assume </span><a NAME="E1:21"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
 <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c2">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c3">b2</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="nat_3.html#K7" title="NAT_3:func.7">Product</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Maroon" title="c2">b1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Maroon" title="c3">b2</font></span>)</span></span><br/>

<a NAME="E2:21"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
 <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c2">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="number08.html#T15" target="_self" onmouseover="rs('number08/T15')" onmouseout="rh()">Th15</a></span>;<br/>
<a NAME="E3:21"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
 <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c3">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:21"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="number08.html#T15" target="_self" onmouseover="rs('number08/T15')" onmouseout="rh()">Th15</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">f0</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <span class="kw"> such that </span><br/><a NAME="E5:21"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
 <a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <font color="Maroon" title="c5">f0</font>
 <span class="kw">and </span><br/><a NAME="E6:21"/><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<font color="Maroon" title="c5">f0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_3.html#D5" onmouseover="rs('nat_3/D5')" onmouseout="rh()">NAT_3:def 5</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">f1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <span class="kw"> such that </span><br/><a NAME="E8:21"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
 <a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Maroon" title="c2">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <font color="Maroon" title="c6">f1</font>
 <span class="kw">and </span><br/><a NAME="E9:21"/><span class="lab"><font color="Green" title="E35">A7</font></span>: 
<font color="Maroon" title="c6">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c2">b1</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_3.html#D5" onmouseover="rs('nat_3/D5')" onmouseout="rh()">NAT_3:def 5</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">f2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <span class="kw"> such that </span><br/><a NAME="E11:21"/><span class="lab"><font color="Green" title="E36">A8</font></span>: 
 <a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Maroon" title="c3">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <font color="Maroon" title="c7">f2</font>
 <span class="kw">and </span><br/><a NAME="E12:21"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<font color="Maroon" title="c7">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b2</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c3">b2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_3.html#D5" onmouseover="rs('nat_3/D5')" onmouseout="rh()">NAT_3:def 5</a></span>;<br/>
<a NAME="E13:21"/><span class="lab"><font color="Green" title="E38">A10</font></span>: 
<font color="Maroon" title="c6">f1</font> is  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">f1</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/>
<a NAME="E14:21"/><span class="lab"><font color="Green" title="E39">A11</font></span>: 
<font color="Maroon" title="c7">f2</font> is  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">f2</font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" onmouseover="rs('card_1/D7')" onmouseout="rh()">CARD_1:def 7</a></span>;<br/>
<a NAME="E15:21"/><span class="lab"><font color="Green" title="E40">A12</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span></span>)</span></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"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="number08.html#T13" target="_self" onmouseover="rs('number08/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<a NAME="E16:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A13</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">f0</font> <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="c6">f1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E9:21"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="number08.html#T13" target="_self" onmouseover="rs('number08/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<a NAME="E17:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A14</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">f0</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="c6">f1</font>
 
<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="E18:21"/><span class="lab"><font color="Green" title="E43">A15</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">f0</font> <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">f2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E12:21"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="txt" href="#E15:21"><span class="lab"><font color="Green" title="E40">A12</font></span></a>, <a class="ref" href="number08.html#T13" target="_self" onmouseover="rs('number08/T13')" onmouseout="rh()">Th13</a></span>;<br/>
<a NAME="E19:21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A16</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">f0</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="c7">f2</font>
 
<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="E20:21"/><span class="lab"><font color="Green" title="E45">A17</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">f0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">f2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:21"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="txt" href="#E18:21"><span class="lab"><font color="Green" title="E43">A15</font></span></a></span>;<br/>
<a NAME="E21:21"/>
 for <font color="Olive" title="b1">c</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">c</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="c5">f0</font> holds <br/><font color="Maroon" title="c5">f0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font></span>)</span>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="21_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">c</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="c8">c</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="c5">f0</font> implies <font color="Maroon" title="c5">f0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:21_1"/><span class="lab"><font color="Green" title="E46">A18</font></span>: 
<font color="Maroon" title="c8">c</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="c5">f0</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"> <font color="Maroon" title="c5">f0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c9">x</font> = <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font>;<br/>
<a NAME="E2:21_1"/><span class="lab"><font color="Green" title="E47">A19</font></span>: 
<font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E9:21"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="txt" href="#E16:21"><span class="lab"><font color="Green" title="E41">A13</font></span></a>, <a class="txt" href="#E1:21_1"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="funct_1.html#T12" onmouseover="rs('funct_1/T12')" onmouseout="rh()">FUNCT_1:12</a></span>;<br/>
<a NAME="E3:21_1"/><span class="lab"><font color="Green" title="E48">A20</font></span>: 
<font color="Maroon" title="c7">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="txt" href="#E12:21"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="txt" href="#E18:21"><span class="lab"><font color="Green" title="E43">A15</font></span></a>, <a class="txt" href="#E1:21_1"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="funct_1.html#T12" onmouseover="rs('funct_1/T12')" onmouseout="rh()">FUNCT_1:12</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c5">f0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:21"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="txt" href="#E1:21_1"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="funct_1.html#T12" onmouseover="rs('funct_1/T12')" onmouseout="rh()">FUNCT_1:12</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">f1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">f2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:21_1"><span class="lab"><font color="Green" title="E47">A19</font></span></a>, <a class="txt" href="#E3:21_1"><span class="lab"><font color="Green" title="E48">A20</font></span></a>, <a class="ref" href="valued_1.html#T5" onmouseover="rs('valued_1/T5')" onmouseout="rh()">VALUED_1:5</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="E22:21"/><span class="kw">then </span>
<font color="Maroon" title="c5">f0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">f1</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c7">f2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:21"><span class="lab"><font color="Green" title="E45">A17</font></span></a>, <a class="ref" href="valued_1.html#D4" onmouseover="rs('valued_1/D4')" onmouseout="rh()">VALUED_1:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:21"/>
 <a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">b1</font> <a href="valued_1.html#K18" title="VALUED_1:func.18">(#)</a> <font color="Maroon" title="c3">b2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Maroon" title="c2">b1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="nat_3.html#K7" title="NAT_3:func.7">Product</a> <font color="Maroon" title="c3">b2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:21"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="txt" href="#E8:21"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E11:21"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="txt" href="#E13:21"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="txt" href="#E14:21"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="txt" href="#E17:21"><span class="lab"><font color="Green" title="E42">A14</font></span></a>, <a class="txt" href="#E19:21"><span class="lab"><font color="Green" title="E44">A16</font></span></a>, <a class="ref" href="newton04.html#T63" onmouseover="rs('newton04/T63')" onmouseout="rh()">NEWTON04:63</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>
