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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="finseq_2.html#M2">Element</a> of 3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">F<sub>1</sub></font>()) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() = <font color="Maroon">F<sub>2</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>,<span class="p1">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="funct_1.html#K1">.</a> 3</span>)</span>);<br/>
<b>consider </b><font color="Maroon">c<sub>1</sub></font> being   <a href="funct_2.html#NM1">Function</a> of 3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E2:73_1"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_2.html#M2">Element</a> of 3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">F<sub>1</sub></font>() 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>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span> as    <a href="finseq_2.html#M2">Element</a> of 3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">F<sub>1</sub></font>() <b>by </b><i><a class="ref" href="finseq_2.html#T124">FINSEQ_2:124</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#K7">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span> = 
<font color="Maroon">F<sub>2</sub></font>(<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 3</span>)</span>)
<b>by </b><i><a class="txt" href="circcmb3.html#E2:73_1"><i><font color="Green">E34</font></i></a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 2</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 3</span>)</span>)
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 3</span>)</span>)
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>)
<b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</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 3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>();<br/>

<b>assume </b><b>that </b><br/><a NAME="E4:73_1"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>)
 <b>and </b><br/><a NAME="E5:73_1"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>)
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="finseq_2.html#M2">Element</a> of 3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">F<sub>1</sub></font>();<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E2:73_1_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T123">FINSEQ_2:123</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>2</sub></font>(<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>)
<b>by </b><i><a class="txt" href="circcmb3.html#E4:73_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="circcmb3.html#E2:73_1_2"><i><font color="Green">E37</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="circcmb3.html#E5:73_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="circcmb3.html#E2:73_1_2"><i><font color="Green">E37</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:73_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/>


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