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<b>let </b><font color="Maroon" title="c1">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>;<br/><b>let </b><font color="Maroon" title="c3">p</font> be    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of <font color="Maroon" title="c2">R</font>;<br/>





<b>assume </b><a NAME="E1:4"/>
<font color="Maroon" title="c1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">p</font>
 ;<br/>

<a NAME="E2:4"/><b>then </b><i><font color="Green" title="E5">A1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font> &amp; <font color="Maroon" title="c1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">p</font> )
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">q</font> = <font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c1">k</font>;<br/>
<b>take </b>
<font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c1">k</font>
;<br/>

<b>thus </b><a NAME="E3:4"/>
<font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c1">k</font> is    <a href="rewrite1.html#M1" title="REWRITE1:mode.1">RedSequence</a> of <font color="Maroon" title="c2">R</font>
 <b>by </b><i><a class="txt" href="rewrite2.html#E2:4"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="rewrite2.html#T3" target="_self" title="REWRITE2:th.3">Th3</a></i>;<br/>

<b>thus </b><a NAME="E4:4"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font>
 <b>by </b><i><a class="txt" href="rewrite2.html#E2:4"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a></i>;<br/>

<b>hence </b><a NAME="E5:4"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c1">k</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="finseq_1.html#K16" title="FINSEQ_1:func.16">|</a> <font color="Maroon" title="c1">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">k</font> )
 <b>by </b><i><a class="txt" href="rewrite2.html#E2:4"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="finseq_3.html#T121" title="FINSEQ_3:th.121">FINSEQ_3:121</a></i>;<br/>


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