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

<span class="kw">let </span><font color="Maroon" title="c1">d</font>, <font color="Maroon" title="c2">e</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">p</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  st <font color="Olive" title="b1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 &amp; <font color="Maroon" title="c1">d</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">e</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/> <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">d</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">e</font></span>)</span>,<font color="Olive" title="b1">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<font color="Maroon" title="c2">e</font>,<font color="Olive" title="b1">p</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 &amp; <font color="Maroon" title="c1">d</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">e</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">d</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">e</font></span>)</span>,<font color="Maroon" title="c3">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">p</font>) )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:41"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2
 <span class="kw">and </span><br/><a NAME="E2:41"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c1">d</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">and </span><br/><a NAME="E3:41"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
<font color="Maroon" title="c2">e</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c3">p</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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">d</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">e</font></span>)</span>,<font color="Maroon" title="c3">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">p</font>)</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">d2</font> = <font color="Maroon" title="c1">d</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a> , <font color="Maroon" title="c5">e</font> = <font color="Maroon" title="c2">e</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">fp</font> = <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d2</font>,<font color="Maroon" title="c5">e</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">fp</font> = <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon" title="c4">d2</font>,<font color="Maroon" title="c5">e</font></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</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#T13" title="FINSEQ_2:th.13">FINSEQ_2:13</a></span>;<br/>
<a NAME="E6:41"/>
 not <font color="Maroon" title="c3">p</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="txt" href="int_5.html#E33"><span class="lab"><font color="Green" title="E26">Lm3</font></span></a></span>;<br/>
<a NAME="E7:41"/><span class="kw">then </span>
<font color="Maroon" title="c1">d</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c3">p</font> <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="ref" href="int_1.html#T62" title="INT_1:th.62">INT_1:62</a></span>;<br/>
<a NAME="E8:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A4</font></span>: 
 <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">d</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span>,<font color="Maroon" title="c3">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_5.html#T26" target="_self" title="INT_5:th.26">Th26</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">p</font> = <font color="Maroon" title="c3">p</font> as   <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">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="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<a NAME="E10:41"/>
 for <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</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="c7">fp</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c9">k</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="c7">fp</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<span class="kw">assume </span><a NAME="E1:41_1"/>
<font color="Maroon" title="c9">k</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="c7">fp</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<a NAME="E2:41_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">fp</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="E3:41_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A5</font></span>: 
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_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="E1:41_1_1"/>
( <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41_1"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="finseq_1.html#T2" title="FINSEQ_1:th.2">FINSEQ_1:2</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:41_1_1_1"/>
<font color="Maroon" title="c9">k</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="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><div class="add"><a NAME="E2:41_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">d</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/><span class="kw">hence </span><a NAME="E3:41_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:41"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="wsierp_1.html#T7" title="WSIERP_1:th.7">WSIERP_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:41_1_1_2"/>
<font color="Maroon" title="c9">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:41_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c9">k</font></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">fr</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E12:41"/><span class="lab"><font color="Green" title="E36">A6</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">fr</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">fp</font>
 <span class="kw">and </span><br/><a NAME="E13:41"/><span class="lab"><font color="Green" title="E37">A7</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</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="c9">fr</font> holds <br/><font color="Maroon" title="c9">fr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">k</font></span>)</span>,<font color="Maroon" title="c8">p</font>)
 <span class="kw">and </span><br/><a NAME="E14:41"/><span class="lab"><font color="Green" title="E38">A8</font></span>: 
 <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><a href="wsierp_1.html#K4" title="WSIERP_1:func.4">Product</a> <font color="Maroon" title="c7">fp</font></span>)</span>,<font color="Maroon" title="c8">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c9">fr</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="int_5.html#T34" target="_self" title="INT_5:th.34">Th34</a></span>;<br/>
<a NAME="E15:41"/><span class="lab"><font color="Green" title="E39">A9</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">fr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:41"><span class="lab"><font color="Green" title="E36">A6</font></span></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E16:41"/><span class="kw">then </span>
2 <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="c9">fr</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<a NAME="E17:41"/><span class="kw">then </span>
<font color="Maroon" title="c9">fr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2</span>)</span>,<font color="Maroon" title="c8">p</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:41"><span class="lab"><font color="Green" title="E37">A7</font></span></a></span>;<br/>
<a NAME="E18:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A10</font></span>: 
<font color="Maroon" title="c9">fr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c8">p</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E19:41"/>
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="c9">fr</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:41"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="finseq_3.html#T25" title="FINSEQ_3:th.25">FINSEQ_3:25</a></span>;<br/>
<a NAME="E20:41"/><span class="kw">then </span>
<font color="Maroon" title="c9">fr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c7">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c8">p</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:41"><span class="lab"><font color="Green" title="E37">A7</font></span></a></span>;<br/>
<a NAME="E21:41"/><span class="kw">then </span>
<font color="Maroon" title="c9">fr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">d</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span>,<font color="Maroon" title="c8">p</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E22:41"/><span class="kw">then </span>
<font color="Maroon" title="c9">fr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default">1,<span class="p2">(<span class="default"><a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c8">p</font>)</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:41"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="txt" href="#E15:41"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="txt" href="#E18:41"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E23:41"/><span class="kw">then </span>
 <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c9">fr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<font color="Maroon" title="c5">e</font>,<font color="Maroon" title="c8">p</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_1.html#T99" title="RVSUM_1:th.99">RVSUM_1:99</a></span>;<br/>
<span class="kw">hence </span><a NAME="E24:41"/>
 <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">d</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c2">e</font></span>)</span>,<font color="Maroon" title="c3">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> (<font color="Maroon" title="c2">e</font>,<font color="Maroon" title="c3">p</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:41"><span class="lab"><font color="Green" title="E38">A8</font></span></a>, <a class="ref" href="rvsum_1.html#T99" title="RVSUM_1:th.99">RVSUM_1:99</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
