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<b>let </b><font color="Maroon" title="c1">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of <font color="Maroon" title="c1">D</font>;<br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E9">A1</font></i>: 
(  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">D</font> &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  is   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> &amp; <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c3">m0</font> = <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> ;<br/>
<a NAME="E3:11"/><i><font color="Green" title="E10">A2</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="prgcor_2.html#K4" title="PRGCOR_2:func.4">XFS2FS*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m0</font> &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">m0</font> holds <br/><span class="p1">(<span class="default"><a href="prgcor_2.html#K4" title="PRGCOR_2:func.4">XFS2FS*</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> ) )
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:11"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="prgcor_2.html#D4" target="_self" title="PRGCOR_2:def.4">Def4</a></i>;<br/>
<a NAME="E4:11"/><i><font color="Green" title="E11">A3</font></i>: 
<font color="Maroon" title="c3">m0</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="txt" href="prgcor_2.html#E1:11"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="nat_1.html#T45" title="NAT_1:th.45">NAT_1:45</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">q</font> =  <a href="prgcor_2.html#K4" title="PRGCOR_2:func.4">XFS2FS*</a> <font color="Maroon" title="c2">p</font>;<br/>
<b>thus </b><a NAME="E5:11"/>
<font color="Maroon" title="c2">p</font> <a href="prgcor_2.html#R1" title="PRGCOR_2:pred.1">is_an_xrep_of</a>  <a href="prgcor_2.html#K4" title="PRGCOR_2:func.4">XFS2FS*</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="prgcor_2.html#E1:11"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="prgcor_2.html#E3:11"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="prgcor_2.html#E4:11"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="prgcor_2.html#D5" target="_self" title="PRGCOR_2:def.5">Def5</a></i>;<br/>


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