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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">nt</font>, <font color="Olive" title="b2">nt1</font> being   <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>   st  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">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="Olive" title="b2">nt1</font> &amp; <font color="Olive" title="b1">nt</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> holds <br/><font color="Olive" title="b2">nt1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a></span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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> &amp; <font color="Maroon" title="c2">nt</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> implies <font color="Maroon" title="c3">nt1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> )</span><br/>





<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E35">A1</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> &amp; <font color="Maroon" title="c2">nt</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">nt1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">without_repeated_line</a></span><br/>

<a NAME="E2:37"/>
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">nt</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">nt1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 
<b>by </b><i><a class="ref" href="finseq_2.html#T109" title="FINSEQ_2:th.109">FINSEQ_2:109</a></i>;<br/>
<b>hence </b><a NAME="E3:37"/>
<font color="Maroon" title="c3">nt1</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#E1:37"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="finseq_4.html#T76" title="FINSEQ_4:th.76">FINSEQ_4:76</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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