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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">a</font> being  <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> &amp; ( ( <font color="Maroon">a<sub>2</sub></font> is  not   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> &amp; <font color="Maroon">a<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 ) or  ex <font color="Olive">t</font> being  <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> &amp; <font color="Maroon">a<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Olive">t</font> ) ) );<br/>
<a NAME="E1:60_1_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/>for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   ex <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>,<font color="Olive">x</font>,<font color="Olive">y</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:60_1_1_1"/><i><font color="Green">E35</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font>
 ;<br/>

<b>assume </b><a NAME="E2:60_1_1_1"/>
<font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<a NAME="E3:60_1_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E4:60_1_1_1"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="txt" href="abcmiz_0.html#E1:60_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E5:60_1_1_1"/><b>then </b>
( <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">p</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> the <a href="abcmiz_0.html#U1" target="_self">adjectives</a> of <font color="Maroon">T</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T12">FUNCT_1:12</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">T</font> ;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_1_1_1"/>
(  not <font color="Maroon">x</font> is   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> or <font color="Maroon">x</font> is   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">x</font> is  not   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>
 ;<br/><div class="add"><b>take </b>
0
;<br/><b>take </b>
<font color="Maroon">a</font>
;<br/><b>thus </b><a NAME="E2:60_1_1_1_1_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; ( ( <font color="Maroon">x</font> is  not   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> &amp; 0 <a href="hidden.html#R1">=</a> 0 ) or  ex <font color="Olive">t</font> being  <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; 0 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Olive">t</font> ) ) )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_2"/>
<font color="Maroon">x</font> is   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">t</font> = <font color="Maroon">x</font> as   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> ;<br/><b>take </b>
<font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Maroon">t</font>
;<br/><b>take </b>
<font color="Maroon">a</font>
;<br/><b>thus </b><a NAME="E3:60_1_1_1_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/><b>thus </b><a NAME="E4:60_1_1_1_1_2"/>
( ( <font color="Maroon">x</font> is  not   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> &amp; <font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> 0 ) or  ex <font color="Olive">t</font> being  <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Olive">t</font> ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E2:60_1_1"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/>for <font color="Olive">x</font>, <font color="Olive">y1</font>, <font color="Olive">y2</font> being   <a href="hidden.html#M1">set</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>,<font color="Olive">x</font>,<font color="Olive">y1</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">n</font>,<font color="Olive">x</font>,<font color="Olive">y2</font>] holds <br/><font color="Olive">y1</font> <a href="hidden.html#R1">=</a> <font color="Olive">y2</font>
 
;<br/>
<b>consider </b><font color="Maroon">q</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><br/><a NAME="E4:60_1_1"/><i><font color="Green">E47</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>and </b><br/><a NAME="E5:60_1_1"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> or <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 0 )
 <b>and </b><br/><a NAME="E6:60_1_1"/><i><font color="Green">E49</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">i</font> &amp; <font color="Olive">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">i</font>,<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>,<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>]
 <b>from </b><i><a class="ref" href="recdef_1.html#S5">RECDEF_1:sch 5</a>(, <a class="txt" href="abcmiz_0.html#E1:60_1_1"><i><font color="Green">E32</font></i></a>);<br/></i>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q</font> implies <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>1</sub></font> is   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> );<br/>
<a NAME="E7:60_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[0]
 
<b>by </b><i><a class="ref" href="finseq_3.html#T26">FINSEQ_3:26</a></i>;<br/>
<div><i><font color="Green">E51</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:60_1_1_2"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">k</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:60_1_1_2_1"/>
<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q</font>
 ;<br/><a NAME="E2:60_1_1_2_1"/><b>then </b>
( ( <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies <font color="Maroon">k</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) &amp; <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> )
 <b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E3:60_1_1_2_1"/><b>then </b><i><font color="Green">E53</font></i>: 
( ( <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies <font color="Maroon">k</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1 ) &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> )
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:60_1_1_2_1"/><b>then </b>
( <font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 implies  ex <font color="Olive">a</font> being  <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> &amp; ( ( <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> is  not   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> &amp; <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0 ) or  ex <font color="Olive">t</font> being  <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> &amp; <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Olive">t</font> ) ) ) )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E5:60_1_1_2_1"/>
<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>
 <b>by </b><i>, , , <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:60_1_1_2"/>
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E9:60_1_1"/><i><font color="Green">E110</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(, );<br/></i>
<a NAME="E10:60_1_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">q</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:60_1_1_3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">q</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:60_1_1_3"/><i><font color="Green">E111</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">q</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:60_1_1_3"/>
<font color="Maroon">a</font> is   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:60_1_1_3"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">q</font> = <font color="Maroon">q</font> as    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon">q</font>
;<br/>

<b>thus </b><a NAME="E12:60_1_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 <b>by </b><i>, </i>;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">t</font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><a NAME="E13:60_1_1"/><i><font color="Green">E112</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 ;<br/>

<a NAME="E14:60_1_1"/><b>then </b>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E15:60_1_1"/><b>then </b>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E16:60_1_1"/><b>then </b>
 ex <font color="Olive">a</font> being  <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; ( ( <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is  not   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> &amp; <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> 0 ) or  ex <font color="Olive">t</font> being  <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Olive">t</font> ) ) )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E17:60_1_1"/>
<font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="abcmiz_0.html#K5" target="_self">ast</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/>


</div>
