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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">nt</font>, <font color="Maroon" title="c3">nt1</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <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> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:33"/><i><font color="Green" title="E31">A1</font></i>: 
( <font color="Maroon" title="c2">nt</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> &amp; <font color="Maroon" title="c3">nt1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> )
 <b>and </b><br/><a NAME="E2:33"/><i><font color="Green" title="E32">A2</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">nt1</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">nt'</font> = <font color="Maroon" title="c2">nt</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> ;<br/>
<a NAME="E4:33"/>
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">nt1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">nt'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">nt1</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">nt'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">nt</font> )
 
<b>by </b><i><a class="txt" href="matrix13.html#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="matrix13.html#E2:33"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="finseq_2.html#T144" title="FINSEQ_2:th.144">FINSEQ_2:144</a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>;<br/>
<a NAME="E5:33"/><b>then </b><i><font color="Green" title="E33">A3</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">nt'</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">nt'</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">nt1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T46" title="RELAT_1:th.46">RELAT_1:46</a>, <a class="ref" href="relat_1.html#T47" title="RELAT_1:th.47">RELAT_1:47</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">nn</font> = <font color="Maroon" title="c4">nt'</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">nt1</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font>, <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="ref" href="funct_2.html#T3" title="FUNCT_2:th.3">FUNCT_2:3</a></i>;<br/>
<a NAME="E7:33"/>
<font color="Maroon" title="c4">nt'</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a>
 
<b>by </b><i><a class="txt" href="matrix13.html#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="funct_1.html#T62" title="FUNCT_1:th.62">FUNCT_1:62</a></i>;<br/>
<a NAME="E8:33"/><b>then </b>
( <font color="Maroon" title="c5">nn</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> &amp; <font color="Maroon" title="c5">nn</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> )
 
<b>by </b><i><a class="txt" href="matrix13.html#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="matrix13.html#E5:33"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="funct_1.html#T46" title="FUNCT_1:th.46">FUNCT_1:46</a>, <a class="ref" href="funct_2.html#D3" title="FUNCT_2:def.3">FUNCT_2:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">nn</font> = <font color="Maroon" title="c5">nn</font> as   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">nn</font>
;<br/>

<b>thus </b><font color="Maroon" title="c2">nt</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c6">nn</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">nt</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c4">nt'</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">nt1</font>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p2">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">nt1</font></span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">nt1</font>
<b>by </b><i><a class="txt" href="matrix13.html#E1:33"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="matrix13.html#E2:33"><i><font color="Green" title="E32">A2</font></i></a>, <a class="ref" href="funct_1.html#T61" title="FUNCT_1:th.61">FUNCT_1:61</a></i>
<br/>.= 
<font color="Maroon" title="c3">nt1</font>
<b>by </b><i><a class="ref" href="relat_1.html#T80" title="RELAT_1:th.80">RELAT_1:80</a></i>
;<br/>


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