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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> = <a href="comput_1.html#K18" target="_self">[*]</a>  <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="comput_1.html#K7" target="_self">succ</a> 1</span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p4"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p5"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p0">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span>,<span class="p3">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 2</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  = <font color="Maroon">a<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="nat_1.html#NM1">Nat</a>,  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>  <a href="nat_1.html#NM1">Nat</a> = <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(  <a href="nat_1.html#NM1">Nat</a>,  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  = <font color="Maroon">a<sub>1</sub></font> <a href="nat_1.html#K2">*</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(  <a href="nat_1.html#NM1">Nat</a>,  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>));<br/>
<b>deffunc </b><font color="Maroon">H<sub>5</sub></font>(  <a href="nat_1.html#NM1">Nat</a>,  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>  <a href="nat_1.html#NM1">Nat</a> = <font color="Maroon">a<sub>2</sub></font>;<br/>
<a NAME="E1:172"/><i><font color="Green">E106</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <a href="comput_1.html#K18" target="_self">[*]</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>)
 
<b>by </b><i><a class="ref" href="comput_1.html#T90" target="_self">Th90</a></i>;<br/>
<a NAME="E2:172"/><i><font color="Green">E107</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default">1 <a href="comput_1.html#K7" target="_self">succ</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="binarith.html#K13">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="172_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="binarith.html#K13">*&gt;</a></span> as    <a href="finseq_2.html#M2">Element</a> of 1 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  ;<br/>
<b>thus </b><span class="p1">(<span class="default">1 <a href="comput_1.html#K7" target="_self">succ</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="binarith.html#K13">*&gt;</a></span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="comput_1.html#D10" target="_self">Def10</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="finseq_4.html#T25">FINSEQ_4:25</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E3:172"/><i><font color="Green">E108</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="172_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> as    <a href="finseq_2.html#M2">Element</a> of 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T121">FINSEQ_2:121</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="comput_1.html#K2" target="_self">.</a> 1
<b>by </b><i><a class="ref" href="comput_1.html#T42" target="_self">Th42</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E4:172"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="comput_1.html#K7" target="_self">succ</a> 1</span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p4">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>))
 
<b>from </b><i><a class="ref" href="comput_1.html#S1" target="_self">COMPUT_1:sch 1</a>(<a class="txt" href="comput_1.html#E2:172"><i><font color="Green">E107</font></i></a>, <a class="txt" href="comput_1.html#E3:172"><i><font color="Green">E108</font></i></a>);<br/></i>
<a NAME="E5:172"/><b>then </b><i><font color="Green">E109</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="comput_1.html#K7" target="_self">succ</a> 1</span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p4">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>)
 
;<br/>
<a NAME="E6:172"/><i><font color="Green">E110</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 2</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="172_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> as    <a href="finseq_2.html#M2">Element</a> of 2 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T121">FINSEQ_2:121</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 2</span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> = 
<font color="Maroon">c<sub>5</sub></font> <a href="comput_1.html#K2" target="_self">.</a> 2
<b>by </b><i><a class="ref" href="comput_1.html#T42" target="_self">Th42</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E7:172"/><i><font color="Green">E111</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><a href="comput_1.html#K18" target="_self">[*]</a>  <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="comput_1.html#K7" target="_self">succ</a> 1</span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p0"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p1">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span>,<span class="p4">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 2</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">H<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>),<font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>))
 
<b>from </b><i><a class="ref" href="comput_1.html#S2" target="_self">COMPUT_1:sch 2</a>(<a class="txt" href="comput_1.html#E1:172"><i><font color="Green">E106</font></i></a>, <a class="txt" href="comput_1.html#E5:172"><i><font color="Green">E109</font></i></a>, <a class="txt" href="comput_1.html#E6:172"><i><font color="Green">E110</font></i></a>);<br/></i>
<a NAME="E8:172"/><i><font color="Green">E112</font></i>: 
 <a href="comput_1.html#K3" target="_self">arity</a> <span class="p1">(<span class="default"><a href="comput_1.html#K18" target="_self">[*]</a>  <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="comput_1.html#K7" target="_self">succ</a> 1</span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p0"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p1">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span>,<span class="p4">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 2</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="comput_1.html#D26" target="_self">Def26</a></i>;<br/>
<a NAME="E9:172"/><i><font color="Green">E113</font></i>: 
 <a href="comput_1.html#K3" target="_self">arity</a> <span class="p1">(<span class="default">0 <a href="comput_1.html#K6" target="_self">const</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="comput_1.html#T35" target="_self">Th35</a></i>;<br/>
<a NAME="E10:172"/>
0 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="comput_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E11:172"/><b>then </b><i><font color="Green">E114</font></i>: 
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> 0 <a href="finseq_2.html#K4">-tuples_on</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means <a href="comput_1.html#K19" target="_self">[!]</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="binarith.html#K13">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> <a href="newton.html#K12">!</a> ;<br/>
<a NAME="E12:172"/><i><font color="Green">E115</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="172_4"><b>proof </b></a><div class="add">

<b>thus </b><a href="comput_1.html#K19" target="_self">[!]</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default">0</span><a href="binarith.html#K13">*&gt;</a></span> = 
<span class="p1">(<span class="default">0 <a href="comput_1.html#K6" target="_self">const</a> 1</span>)</span> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="txt" href="comput_1.html#E9:172"><i><font color="Green">E113</font></i></a>, <a class="ref" href="comput_1.html#T84" target="_self">Th84</a></i>
<br/>.= 
0 <a href="newton.html#K12">!</a> 
<b>by </b><i><a class="txt" href="comput_1.html#E11:172"><i><font color="Green">E114</font></i></a>, <a class="ref" href="comput_1.html#T36" target="_self">Th36</a>, <a class="ref" href="newton.html#T18">NEWTON:18</a></i>
;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E116</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="172_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:172_5"/><i><font color="Green">E117</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">c<sub>3</sub></font>]
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="newton.html#K12">!</a>  as   <a href="nat_1.html#NM1">Nat</a> ;<br/><a href="comput_1.html#K19" target="_self">[!]</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span><a href="binarith.html#K13">*&gt;</a></span> = 
<span class="p1">(<span class="default"><a href="comput_1.html#K18" target="_self">[*]</a>  <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="comput_1.html#K7" target="_self">succ</a> 1</span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p5"><a href="funct_6.html#K6">&lt;:</a><span class="default"><span class="p0"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p1">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 1</span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span>,<span class="p4">(<span class="default">2 <a href="comput_1.html#K8" target="_self">proj</a> 2</span>)</span></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="funct_6.html#K6">:&gt;</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="finseq_4.html#K2">*&gt;</a></span>
<b>by </b><i><a class="txt" href="comput_1.html#E8:172"><i><font color="Green">E112</font></i></a>, <a class="txt" href="comput_1.html#E9:172"><i><font color="Green">E113</font></i></a>, <a class="txt" href="comput_1.html#E1:172_5"><i><font color="Green">E117</font></i></a>, <a class="ref" href="comput_1.html#T86" target="_self">Th86</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="comput_1.html#E7:172"><i><font color="Green">E111</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="newton.html#K12">!</a> 
<b>by </b><i><a class="ref" href="newton.html#T21">NEWTON:21</a></i>
;<br/><b>hence </b><a NAME="E4:172_5"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E14:172"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="comput_1.html#E12:172"><i><font color="Green">E115</font></i></a>, <a class="txt" href="comput_1.html#E13:172"><i><font color="Green">E116</font></i></a>);<br/></i>
<b>hence </b><a NAME="E15:172"/>
<a href="comput_1.html#K19" target="_self">[!]</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="binarith.html#K13">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="binarith.html#K13">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K12">!</a> 
 ;<br/>


</div>
