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

<span class="kw">let </span><font color="Maroon" title="c1">n</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="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="stirl2_1.html#K3" title="STIRL2_1:func.3">block</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 3</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><span class="p1">(<span class="default">$1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="stirl2_1.html#K3" title="STIRL2_1:func.3">block</a> $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">$1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">$1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 3</span>)</span>;<br/>
<a NAME="E1:79"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
2 <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#D3" title="NEWTON:def.3">NEWTON:def 3</a></span>;<br/>
<a NAME="E2:79"/><span class="lab"><font color="Green" title="E45">A2</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="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:79_1"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">k</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="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1]</span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">k1</font> = <font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">k2</font> = <font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">k3</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1;<br/>
<span class="lab"><font color="Green" title="E47">A4</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="stirl2_1.html#K3" title="STIRL2_1:func.3">block</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="stirl2_1.html#T62" target="_self" title="STIRL2_1:th.62">Th62</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K17" title="BINOP_2:func.17">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 2</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="stirl2_1.html#T61" target="_self" title="STIRL2_1:th.61">Th61</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K17" title="BINOP_2:func.17">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 12</span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span>

;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="stirl2_1.html#K3" title="STIRL2_1:func.3">block</a> <font color="Maroon" title="c2">k</font> = 
<span class="p1">(<span class="default">3 <a href="binop_2.html#K17" title="BINOP_2:func.17">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span></span>)</span> <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79_1"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="stirl2_1.html#T61" target="_self" title="STIRL2_1:th.61">Th61</a></span>
<br/>.= 
<span class="p1">(<span class="default">3 <a href="binop_2.html#K17" title="BINOP_2:func.17">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span></span>)</span> <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 6</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="stirl2_1.html#T61" target="_self" title="STIRL2_1:th.61">Th61</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K17" title="BINOP_2:func.17">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">3 <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span> <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span></span>)</span>

;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="stirl2_1.html#K3" title="STIRL2_1:func.3">block</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K17" title="BINOP_2:func.17">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 12</span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span></span>)</span> <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K17" title="BINOP_2:func.17">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span> <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">4 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79_1"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="ref" href="stirl2_1.html#T56" target="_self" title="STIRL2_1:th.56">Th56</a></span>
<br/>.= 
<span class="p1">(<span class="default">3 <a href="binop_2.html#K17" title="BINOP_2:func.17">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 24</span>)</span></span>)</span> <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 6</span>)</span>

<br/>.= 
<span class="p1">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K15" title="BINOP_2:func.15">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K22" title="BINOP_2:func.22">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="binop_2.html#K21" title="BINOP_2:func.21">-</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K18" title="BINOP_2:func.18">/</a> 6</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="stirl2_1.html#T61" target="_self" title="STIRL2_1:th.61">Th61</a></span>
<br/>.= 
<span class="p1">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 3</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="stirl2_1.html#T61" target="_self" title="STIRL2_1:th.61">Th61</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:79_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">k</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1]
 ; <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>
<a NAME="E3:79"/>
2 <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#D3" title="NEWTON:def.3">NEWTON:def 3</a></span>;<br/>
<a NAME="E4:79"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A5</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="stirl2_1.html#T31" target="_self" title="STIRL2_1:th.31">Th31</a></span>;<br/>
<a NAME="E5:79"/>
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S2" title="NAT_1:sch.2">NAT_1:sch 2</a>(<a class="txt" href="#E4:79"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E45">A2</font></span></a>);<br/></span>
<span class="kw">hence </span><a NAME="E6:79"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="stirl2_1.html#K3" title="STIRL2_1:func.3">block</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="newton.html#K8" title="NEWTON:func.8">choose</a> 3</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>
