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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="binarith.html#NM1">Tuple</a> of 2,<a href="circcomb.html#K10">BOOLEAN</a> ) <b>-&gt; </b>   <a href="subset_1.html#M2">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>,<span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 2</span>)</span>);<br/>
<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="funct_2.html#NM1">Function</a> of 2 <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="E1:29_1"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a>  holds <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="finseq_1.html#K10">&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_1.html#K10">*&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>,<font color="Olive">b<sub>2</sub></font>)
 <b>and </b><br/><a NAME="E2:29_1"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M2">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="finseq_1.html#K10">&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_1.html#K10">*&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>,<font color="Olive">b<sub>2</sub></font>)
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="binarith.html#NM1">Tuple</a> of 2,<a href="circcomb.html#K10">BOOLEAN</a> ;<br/><b>consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M2">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> <b> such that </b><br/><a NAME="E2:29_1_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T120">FINSEQ_2:120</a></i>;<br/><b>thus </b><font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> = 
<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>)
<b>by </b><i><a class="txt" href="facirc_1.html#E1:29_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="facirc_1.html#E2:29_1_1"><i><font color="Green">E14</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="facirc_1.html#E2:29_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="facirc_1.html#E2:29_1_1"><i><font color="Green">E14</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:29_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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