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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">d</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">zero</a>  <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="c3">G</font> be    <a href="chain_1.html#M1" title="CHAIN_1:mode.1">Grating</a> of <font color="Maroon" title="c2">d</font>;<br/>





<b>assume </b><a NAME="E1:81"/><i><font color="Green" title="E54">A1</font></i>: 
<font color="Maroon" title="c1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">d</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">C</font> be   <a href="chain_1.html#NM4" title="CHAIN_1:NM.4">Chain</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c3">G</font>;<br/>

<a NAME="E2:81"/>
for <font color="Olive" title="b1">A</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds not <font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="chain_1.html#K11" title="CHAIN_1:func.11">del</a> <font color="Maroon" title="c4">C</font>
 
<b>by </b><i><a class="txt" href="chain_1.html#E1:81"><i><font color="Green" title="E54">A1</font></i></a>, <a class="ref" href="chain_1.html#T52" target="_self" title="CHAIN_1:th.52">Th52</a></i>;<br/>
<b>hence </b><a NAME="E3:81"/>
 <a href="chain_1.html#K11" title="CHAIN_1:func.11">del</a> <font color="Maroon" title="c4">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K6" title="CHAIN_1:func.6">0_</a> <font color="Maroon" title="c1">k</font>,<font color="Maroon" title="c3">G</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>


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