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<span class="kw">let </span><font color="Maroon" title="c1">D</font>, <font color="Maroon" title="c2">C</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/> for <font color="Olive" title="b2">A</font> being  <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c2">C</font>  st <font color="Olive" title="b1">F</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font> holds <br/> <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Olive" title="b1">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">D</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c2">C</font>  st <font color="Maroon" title="c3">F</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font> holds <br/> <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Olive" title="b1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">B</font> be   <a href="rearran1.html#NM1" title="REARRAN1:NM.1">RearrangmentGen</a> of <font color="Maroon" title="c2">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp;  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font> implies  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c3">F</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> 
 <span class="kw">and </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">D</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">fd</font> =  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">p</font> =  <a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">mf</font> =  <a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">h</font> =  <a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">C</font>;<br/>
<a NAME="E3:28"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">C</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="rearran1.html#T12" target="_self" title="REARRAN1:th.12">Th12</a></span>;<br/>
<a NAME="E4:28"/><span class="lab"><font color="Green" title="E27">A4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">fd9</font> =  <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font>, <font color="Maroon" title="c10">F9</font> = <font color="Maroon" title="c3">F</font> as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="finset_1.html#T29" title="FINSET_1:th.29">FINSET_1:29</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">dfd</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c9">fd9</font>, <font color="Maroon" title="c12">dF</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c10">F9</font> as   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E7:28"/><span class="lab"><font color="Green" title="E28">A5</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K16" title="RFUNCT_3:func.16">CHI</a> <font color="Maroon" title="c4">B</font>,<font color="Maroon" title="c2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">B</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K3" title="RFINSEQ:func.3">MIM</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rfinseq.html#D3" title="RFINSEQ:def.3">RFINSEQ:def 3</a>, <a class="ref" href="rfunct_3.html#D6" title="RFUNCT_3:def.6">RFUNCT_3:def 6</a></span>;<br/>
<a NAME="E8:28"/><span class="lab"><font color="Green" title="E29">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="rearran1.html#T13" target="_self" title="REARRAN1:th.13">Th13</a></span>;<br/>
<a NAME="E9:28"/><span class="lab"><font color="Green" title="E30">A7</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> <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> <span class="p2">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E10:28"/><span class="lab"><font color="Green" title="E31">A8</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">B</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="c4">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E11:28"/>
<font color="Maroon" title="c3">F</font> <a href="rfunct_3.html#K22" title="RFUNCT_3:func.22">|</a> <font color="Maroon" title="c1">D</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></span>;<br/>
<a NAME="E12:28"/><span class="kw">then </span>
 <a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font>,<font color="Maroon" title="c3">F</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="#E4:28"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="ref" href="rfunct_3.html#D14" title="RFUNCT_3:def.14">RFUNCT_3:def 14</a></span>;<br/>
<a NAME="E13:28"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c11">dfd</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c12">dF</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#T89" title="CLASSES1:th.89">CLASSES1:89</a></span>;<br/>
<a NAME="E14:28"/><span class="kw">then </span>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E27">A4</font></span></a>, <a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E30">A7</font></span></a></span>;<br/>
<a NAME="E15:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A9</font></span>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E16:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A10</font></span>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<span class="kw">thus </span><a NAME="E17:28"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c13">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> or <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:28_1"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">c</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">C</font><span class="kw"> such that </span><br/><a NAME="E3:28_1"/>
<font color="Maroon" title="c14">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:28_1"/><span class="lab"><font color="Green" title="E34">A11</font></span>: 
<span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#T26" title="PARTFUN1:th.26">PARTFUN1:26</a></span>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <span class="kw">means </span>( $1 <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="c4">B</font> &amp; <font color="Maroon" title="c14">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1 );<br/>
<a NAME="E5:28_1"/><span class="lab"><font color="Green" title="E35">A12</font></span>: 
 ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">take </span><font color="Maroon" title="c15">n</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c15">n</font>]</span><br/>

<a NAME="E1:28_1_1"/>
<font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rearran1.html#T3" target="_self" title="REARRAN1:th.3">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:28_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c15">n</font>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E15:28"><span class="lab"><font color="Green" title="E32">A9</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">consider </span><font color="Maroon" title="c15">mi</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E7:28_1"/><span class="lab"><font color="Green" title="E36">A13</font></span>: 
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c15">mi</font>] &amp; ( for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon" title="c15">mi</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S5" title="NAT_1:sch.5">NAT_1:sch 5</a>(<a class="txt" href="#E5:28_1"><span class="lab"><font color="Green" title="E35">A12</font></span></a>);<br/></span>
<a NAME="E8:28_1"/><span class="lab"><font color="Green" title="E37">A14</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">mi</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<a NAME="E9:28_1"/><span class="kw">then </span>
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c15">mi</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">mi</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T4" title="FINSEQ_2:th.4">FINSEQ_2:4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c16">m1</font> = <font color="Maroon" title="c15">mi</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T5" title="FINSEQ_2:th.5">FINSEQ_2:5</a></span>;<br/>
<a NAME="E11:28_1"/><span class="lab"><font color="Green" title="E38">A15</font></span>: 
<font color="Maroon" title="c15">mi</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_2"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:28_1_2_1"/>
( <font color="Maroon" title="c15">mi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c15">mi</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_2_1_1"><span class="kw">case </span></a><a NAME="E1:28_1_2_1_1"/>
<font color="Maroon" title="c15">mi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span><br/><div class="add"><a NAME="E2:28_1_2_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="rearran1.html#T15" target="_self" title="REARRAN1:th.15">Th15</a></span>;<br/><span class="kw">hence </span><a NAME="E3:28_1_2_1_1"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="txt" href="#E4:28_1"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_1_2_1_2"><span class="kw">case </span></a><a NAME="E1:28_1_2_1_2"/>
<font color="Maroon" title="c15">mi</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span><br/><div class="add"><a NAME="E2:28_1_2_1_2"/><span class="kw">then </span>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c15">mi</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28_1"><span class="lab"><font color="Green" title="E37">A14</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E3:28_1_2_1_2"/><span class="kw">then </span>
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">mi</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E4:28_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A16</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c16">m1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></span>;<br/><a NAME="E5:28_1_2_1_2"/><span class="lab"><font color="Green" title="E40">A17</font></span>: 
<font color="Maroon" title="c16">m1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c15">mi</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></span>;<br/><a NAME="E6:28_1_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">m1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E7:28_1_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">m1</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="c4">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28_1_2_1_2"><span class="lab"><font color="Green" title="E39">A16</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E8:28_1_2_1_2"/><span class="kw">then </span>
not <font color="Maroon" title="c14">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">m1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></span>;<br/><a NAME="E9:28_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A18</font></span>: 
<font color="Maroon" title="c14">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">m1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E10:28_1_2_1_2"/>
<font color="Maroon" title="c16">m1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">B</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28_1"><span class="lab"><font color="Green" title="E38">A15</font></span></a>, <a class="txt" href="#E5:28_1_2_1_2"><span class="lab"><font color="Green" title="E40">A17</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E11:28_1_2_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E4:28_1_2_1_2"><span class="lab"><font color="Green" title="E39">A16</font></span></a>, <a class="txt" href="#E9:28_1_2_1_2"><span class="lab"><font color="Green" title="E41">A18</font></span></a>, <a class="ref" href="rearran1.html#T15" target="_self" title="REARRAN1:th.15">Th15</a></span>;<br/><span class="kw">hence </span><a NAME="E12:28_1_2_1_2"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E10:28"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E4:28_1"><span class="lab"><font color="Green" title="E34">A11</font></span></a>, <a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E36">A13</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E13:28_1"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c13">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> or <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> )</span><br/>

<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <span class="kw">means </span>( $1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">x</font> );<br/>
<span class="kw">assume </span><a NAME="E18:28"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span></span><br/>

<a NAME="E19:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A19</font></span>: 
 ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T11" title="FINSEQ_2:th.11">FINSEQ_2:11</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">mi</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E21:28"/><span class="lab"><font color="Green" title="E35">A20</font></span>: 
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c14">mi</font>] &amp; ( for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon" title="c14">mi</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> ) )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S5" title="NAT_1:sch.5">NAT_1:sch 5</a>(<a class="txt" href="#E19:28"><span class="lab"><font color="Green" title="E34">A19</font></span></a>);<br/></span>
<a NAME="E22:28"/><span class="lab"><font color="Green" title="E36">A21</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">mi</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E35">A20</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<a NAME="E23:28"/><span class="kw">then </span>
 <a href="xxreal_0.html#K4" title="XXREAL_0:func.4">max</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p1">(<span class="default"><font color="Maroon" title="c14">mi</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">mi</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T4" title="FINSEQ_2:th.4">FINSEQ_2:4</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">m1</font> = <font color="Maroon" title="c14">mi</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_2.html#T5" title="FINSEQ_2:th.5">FINSEQ_2:5</a></span>;<br/>
<a NAME="E25:28"/><span class="lab"><font color="Green" title="E37">A22</font></span>: 
<font color="Maroon" title="c14">mi</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E35">A20</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_2"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_2_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:28_2_1"/>
( <font color="Maroon" title="c14">mi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c14">mi</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_2_1_1"><span class="kw">case </span></a><a NAME="E1:28_2_1_1"/><span class="lab"><font color="Green" title="E38">A23</font></span>: 
<font color="Maroon" title="c14">mi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c16">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1;<br/><a NAME="E3:28_2_1_1"/><span class="lab"><font color="Green" title="E39">A24</font></span>: 
<font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E10:28"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="ref" href="rearran1.html#T7" target="_self" title="REARRAN1:th.7">Th7</a></span>;<br/><a NAME="E4:28_2_1_1"/>
<font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E10:28"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E33">A10</font></span></a>, <a class="txt" href="rearran1.html#E14"><span class="lab"><font color="Green" title="E13">Lm5</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">y</font> = <font color="Maroon" title="c16">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28_2_1_1"><span class="lab"><font color="Green" title="E39">A24</font></span></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E6:28_2_1_1"/>
<span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c17">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E3:28_2_1_1"><span class="lab"><font color="Green" title="E39">A24</font></span></a>, <a class="ref" href="rearran1.html#T15" target="_self" title="REARRAN1:th.15">Th15</a></span>;<br/><span class="kw">hence </span><a NAME="E7:28_2_1_1"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E35">A20</font></span></a>, <a class="txt" href="#E1:28_2_1_1"><span class="lab"><font color="Green" title="E38">A23</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="28_2_1_2"><span class="kw">case </span></a><a NAME="E1:28_2_1_2"/><span class="lab"><font color="Green" title="E38">A25</font></span>: 
<font color="Maroon" title="c14">mi</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span></span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c16">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">m1</font></span>)</span>;<br/><a NAME="E3:28_2_1_2"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c14">mi</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:28"><span class="lab"><font color="Green" title="E36">A21</font></span></a>, <a class="txt" href="#E1:28_2_1_2"><span class="lab"><font color="Green" title="E38">A25</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E4:28_2_1_2"/><span class="kw">then </span>
1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c14">mi</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><a NAME="E5:28_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A26</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">m1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></span>;<br/><a NAME="E6:28_2_1_2"/>
<font color="Maroon" title="c15">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E35">A20</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E7:28_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">m1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></span>;<br/><a NAME="E8:28_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A27</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">m1</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E5:28_2_1_2"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="ref" href="rearran1.html#T8" target="_self" title="REARRAN1:th.8">Th8</a></span>;<br/><a NAME="E9:28_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A28</font></span>: 
<font color="Maroon" title="c16">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E10:28_2_1_2"/>
<font color="Maroon" title="c4">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">mi</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E30">A7</font></span></a>, <a class="txt" href="#E10:28"><span class="lab"><font color="Green" title="E31">A8</font></span></a>, <a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E35">A20</font></span></a>, <a class="txt" href="rearran1.html#E14"><span class="lab"><font color="Green" title="E13">Lm5</font></span></a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c17">y</font> = <font color="Maroon" title="c16">y</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">C</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:28_2_1_2"><span class="lab"><font color="Green" title="E41">A28</font></span></a></span>;<br/><a NAME="E12:28_2_1_2"/>
<font color="Maroon" title="c15">m1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c14">mi</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></span>;<br/><a NAME="E13:28_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">m1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:28"><span class="lab"><font color="Green" title="E37">A22</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E14:28_2_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c17">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K21" title="RFUNCT_3:func.21">FinS</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c1">D</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">m1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E28">A5</font></span></a>, <a class="txt" href="#E5:28_2_1_2"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="txt" href="#E8:28_2_1_2"><span class="lab"><font color="Green" title="E40">A27</font></span></a>, <a class="ref" href="rearran1.html#T15" target="_self" title="REARRAN1:th.15">Th15</a></span>;<br/><span class="kw">hence </span><a NAME="E15:28_2_1_2"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E29">A6</font></span></a>, <a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E35">A20</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E27:28"/>
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rearran1.html#K3" title="REARRAN1:func.3">Rland</a> <font color="Maroon" title="c3">F</font>,<font color="Maroon" title="c4">B</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
