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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>),<font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>))</span><br/>

<a NAME="E1:169_1"/>
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D21" target="_self" title="COMPUT_1:def.21">Def24</a></span>;<br/>
<a NAME="E2:169_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#T23" target="_self" title="COMPUT_1:th.23">Th26</a></span>;<br/>
<a NAME="E3:169_1"/>
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D21" target="_self" title="COMPUT_1:def.21">Def24</a></span>;<br/>
<a NAME="E4:169_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A5</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#T23" target="_self" title="COMPUT_1:th.23">Th26</a></span>;<br/>
<a NAME="E5:169_1"/><span class="lab"><font color="Green" title="E103">A6</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p2"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T142" title="FINSEQ_3:th.142">FINSEQ_3:142</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> = 
<font color="Maroon">F<sub>1</sub></font>() <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><span class="p3"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:169_1"><span class="lab"><font color="Green" title="E101">A4</font></span></a>, <a class="txt" href="#E4:169_1"><span class="lab"><font color="Green" title="E102">A5</font></span></a>, <a class="ref" href="finseq_2.html#T101" title="FINSEQ_2:th.101">FINSEQ_2:101</a>, <a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon">F<sub>1</sub></font>() <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F<sub>3</sub></font>() <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:169_1"><span class="lab"><font color="Green" title="E103">A6</font></span></a>, <a class="txt" href="#E2:169_1"><span class="lab"><font color="Green" title="E101">A4</font></span></a>, <a class="txt" href="#E4:169_1"><span class="lab"><font color="Green" title="E102">A5</font></span></a>, <a class="ref" href="finseq_2.html#T101" title="FINSEQ_2:th.101">FINSEQ_2:101</a>, <a class="ref" href="finseq_3.html#T142" title="FINSEQ_3:th.142">FINSEQ_3:142</a></span>
<br/>.= 
<font color="Maroon">F<sub>1</sub></font>() <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>),<span class="p2">(<span class="default"><font color="Maroon">F<sub>3</sub></font>() <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:169"><span class="lab"><font color="Green" title="E99">A2</font></span></a></span>
<br/>.= 
<font color="Maroon">F<sub>1</sub></font>() <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>),<font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:169"><span class="lab"><font color="Green" title="E100">A3</font></span></a></span>
<br/>.= 
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">F<sub>5</sub></font>(<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>),<font color="Maroon">F<sub>6</sub></font>(<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>))
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:169"><span class="lab"><font color="Green" title="E98">A1</font></span></a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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