<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E5">A1</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<a NAME="E2:13"/><i><font color="Green" title="E6">A2</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</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="c1">f</font>
 
<b>by </b><i><a class="ref" href="euclid_2.html#T8" title="EUCLID_2:th.8">EUCLID_2:8</a></i>;<br/>
<a NAME="E3:13"/><i><font color="Green" title="E7">A3</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="ref" href="seq_1.html#D6" title="SEQ_1:def.6">SEQ_1:def 6</a></i>;<br/>
<a NAME="E4:13"/><i><font color="Green" title="E8">A4</font></i>: 
 <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <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"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E2:13"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<a NAME="E5:13"/><b>then </b><i><font color="Green" title="E9">A5</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> &amp;  <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <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"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E6:13"/><i><font color="Green" title="E10">A6</font></i>: 
 <a href="rfinseq2.html#K4" title="RFINSEQ2:func.4">min</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p2">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T66" title="RVSUM_1:th.66">RVSUM_1:66</a></i>;<br/>
<a NAME="E7:13"/><i><font color="Green" title="E11">A7</font></i>: 
 <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <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="c1">f</font>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E2:13"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="rfinseq2.html#E5:13"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E8:13"/><b>then </b><i><font color="Green" title="E12">A8</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<a NAME="E9:13"/><i><font color="Green" title="E13">A9</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p2">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T66" title="RVSUM_1:th.66">RVSUM_1:66</a></i>;<br/>
<a NAME="E10:13"/><i><font color="Green" title="E14">A10</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p2">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rvsum_1.html#T66" title="RVSUM_1:th.66">RVSUM_1:66</a></i>;<br/>
<a NAME="E11:13"/><i><font color="Green" title="E15">A11</font></i>: 
 <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E3:13"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<a NAME="E12:13"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E2:13"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<a NAME="E13:13"/><b>then </b>
<font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E9:13"><i><font color="Green" title="E13">A9</font></i></a>, <a class="txt" href="rfinseq2.html#E10:13"><i><font color="Green" title="E14">A10</font></i></a>, <a class="ref" href="xreal_1.html#T70" title="XREAL_1:th.70">XREAL_1:70</a></i>;<br/>
<a NAME="E14:13"/><b>then </b><i><font color="Green" title="E16">A12</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E8:13"><i><font color="Green" title="E12">A8</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<a NAME="E15:13"/>
 <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E3:13"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<a NAME="E16:13"/><b>then </b><i><font color="Green" title="E17">A13</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E2:13"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<a NAME="E17:13"/>
<font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E7:13"><i><font color="Green" title="E11">A7</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<a NAME="E18:13"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p2">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p2">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="xreal_1.html#T66" title="XREAL_1:th.66">XREAL_1:66</a></i>;<br/>
<a NAME="E19:13"/><b>then </b><i><font color="Green" title="E18">A14</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E9:13"><i><font color="Green" title="E13">A9</font></i></a>, <a class="txt" href="rfinseq2.html#E10:13"><i><font color="Green" title="E14">A10</font></i></a>, <a class="txt" href="rfinseq2.html#E16:13"><i><font color="Green" title="E17">A13</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>
<a NAME="E20:13"/><i><font color="Green" title="E19">A15</font></i>: 
 <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E3:13"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="rfinseq2.html#E4:13"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="rfinseq2.html#E14:13"><i><font color="Green" title="E16">A12</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<a NAME="E21:13"/>
 <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="txt" href="rfinseq2.html#E1:13"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="rfinseq2.html#E2:13"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="rfinseq2.html#E11:13"><i><font color="Green" title="E15">A11</font></i></a>, <a class="txt" href="rfinseq2.html#E19:13"><i><font color="Green" title="E18">A14</font></i></a>, <a class="ref" href="rfinseq2.html#D2" target="_self" title="RFINSEQ2:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E22:13"/>
(  <a href="rfinseq2.html#K4" title="RFINSEQ2:func.4">min</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K4" title="RFINSEQ2:func.4">min</a> <font color="Maroon" title="c1">f</font></span>)</span> &amp;  <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="rvsum_1.html#K10" title="RVSUM_1:func.10">*</a> <font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq2.html#K2" title="RFINSEQ2:func.2">min_p</a> <font color="Maroon" title="c1">f</font> )
 <b>by </b><i><a class="txt" href="rfinseq2.html#E6:13"><i><font color="Green" title="E10">A6</font></i></a>, <a class="txt" href="rfinseq2.html#E20:13"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/>


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