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<b>let </b><font color="Maroon" title="c1">k</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> ;<br/><b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L2" title="STRUCT_0:struct.2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c2">X</font>;<br/>





<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E27">A1</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">k</font>
 ;<br/>

<a NAME="E2:27"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">k</font>
 
<b>by </b><i><a class="ref" href="int_1.html#T20" title="INT_1:th.20">INT_1:20</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c4">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E4:27"/><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c4">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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="lopban_4.html#E1:27"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<a NAME="E5:27"/><i><font color="Green" title="E30">A4</font></i>: 
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1
 
<b>by </b><i><a class="txt" href="lopban_4.html#E4:27"><i><font color="Green" title="E29">A3</font></i></a></i>;<br/>
<a NAME="E6:27"/>
<font color="Maroon" title="c4">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="lopban_4.html#K4" title="LOPBAN_4:func.4">Shift</a> <font color="Maroon" title="c3">seq</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c1">k</font> = 
<font color="Maroon" title="c3">seq</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">m</font>
<b>by </b><i><a class="txt" href="lopban_4.html#E4:27"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="lopban_4.html#D5" target="_self" title="LOPBAN_4:def.5">Def5</a></i>
<br/>.= 
<font color="Maroon" title="c3">seq</font> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="lopban_4.html#E2:27"><i><font color="Green" title="E28">A2</font></i></a>, <a class="txt" href="lopban_4.html#E5:27"><i><font color="Green" title="E30">A4</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>
;<br/><br/>


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