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

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="binarith.html#NM1">Tuple</a> of 1,<a href="circcomb.html#K10">BOOLEAN</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a>  = <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 1</span>)</span>);<br/>
<b>consider </b><font color="Maroon">c<sub>1</sub></font> being   <a href="funct_2.html#NM1">Function</a> of 1 <a href="finseq_2.html#K4">-tuples_on</a> <a href="circcomb.html#K10">BOOLEAN</a> , <a href="circcomb.html#K10">BOOLEAN</a> <b> such that </b><br/><a NAME="E2:3_1"/><i><font color="Green">E1</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="binarith.html#NM1">Tuple</a> of 1,<a href="circcomb.html#K10">BOOLEAN</a>  holds <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<div><b>hereby </b>
<div class="add"><b>take </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> as   <a href="binarith.html#NM1">Tuple</a> of 1,<a href="circcomb.html#K10">BOOLEAN</a>  <b>by </b><i><a class="ref" href="finseq_2.html#T118">FINSEQ_2:118</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> = 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> 1</span>)</span>)
<b>by </b><i><a class="txt" href="gfacirc1.html#E2:3_1"><i><font color="Green">E1</font></i></a></i>
<br/>.= 
<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">c<sub>3</sub></font>)
<b>by </b><i><a class="ref" href="finseq_1.html#D8">FINSEQ_1:def 8</a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="funct_2.html#NM1">Function</a> of 1 <a href="finseq_2.html#K4">-tuples_on</a> <a href="circcomb.html#K10">BOOLEAN</a> , <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:3_1"/><i><font color="Green">E2</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a>  holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>and </b><br/><a NAME="E5:3_1"/><i><font color="Green">E3</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a>  holds <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="binarith.html#NM1">Tuple</a> of 1,<a href="circcomb.html#K10">BOOLEAN</a> ;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> <b> such that </b><br/><a NAME="E2:3_1_2"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="facirc_1.html#K5">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K5">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T117">FINSEQ_2:117</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">c<sub>5</sub></font>)
<b>by </b><i><a class="txt" href="gfacirc1.html#E4:3_1"><i><font color="Green">E2</font></i></a>, <a class="txt" href="gfacirc1.html#E2:3_1_2"><i><font color="Green">E4</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="gfacirc1.html#E5:3_1"><i><font color="Green">E3</font></i></a>, <a class="txt" href="gfacirc1.html#E2:3_1_2"><i><font color="Green">E4</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:3_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


</div>
