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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">zero</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <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"> for <font color="Olive" title="b1">G</font> being   <a href="chain_1.html#M1" title="CHAIN_1:mode.1">Grating</a> of <font color="Maroon" title="c1">d</font><br/> for <font color="Olive" title="b2">C</font> being   <a href="chain_1.html#M3" title="CHAIN_1:mode.3">Cycle</a> of <font color="Maroon" title="c1">d</font>,<font color="Olive" title="b1">G</font> holds  <font color="Olive" title="b2">C</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is    <a href="chain_1.html#M3" title="CHAIN_1:mode.3">Cycle</a> of <font color="Maroon" title="c1">d</font>,<font color="Olive" title="b1">G</font></span><br/><b>let </b><font color="Maroon" title="c2">G</font> be    <a href="chain_1.html#M1" title="CHAIN_1:mode.1">Grating</a> of <font color="Maroon" title="c1">d</font>; <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">C</font> being   <a href="chain_1.html#M3" title="CHAIN_1:mode.3">Cycle</a> of <font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font> holds  <font color="Olive" title="b1">C</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is    <a href="chain_1.html#M3" title="CHAIN_1:mode.3">Cycle</a> of <font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font></span><br/><b>let </b><font color="Maroon" title="c3">C</font> be    <a href="chain_1.html#M3" title="CHAIN_1:mode.3">Cycle</a> of <font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">C</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is    <a href="chain_1.html#M3" title="CHAIN_1:mode.3">Cycle</a> of <font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font></span><br/>





<b>consider </b><font color="Maroon" title="c4">d'</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E2:99"/><i><font color="Green" title="E66">A1</font></i>: 
<font color="Maroon" title="c1">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">d'</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">d'</font> = <font color="Maroon" title="c4">d'</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <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>reconsider </b><font color="Maroon" title="c6">G</font> = <font color="Maroon" title="c2">G</font> as    <a href="chain_1.html#M1" title="CHAIN_1:mode.1">Grating</a> of <font color="Maroon" title="c5">d'</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <b>by </b><i><a class="txt" href="chain_1.html#E2:99"><i><font color="Green" title="E66">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">C</font> = <font color="Maroon" title="c3">C</font> as    <a href="chain_1.html#M3" title="CHAIN_1:mode.3">Cycle</a> of <font color="Maroon" title="c5">d'</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1,<font color="Maroon" title="c6">G</font> <b>by </b><i><a class="txt" href="chain_1.html#E2:99"><i><font color="Green" title="E66">A1</font></i></a></i>;<br/>
<a NAME="E6:99"/>
 <a href="chain_1.html#K10" title="CHAIN_1:func.10">del</a> <font color="Maroon" title="c7">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K11" title="CHAIN_1:func.11">0_</a> <font color="Maroon" title="c5">d'</font>,<font color="Maroon" title="c6">G</font>
 
;<br/>
<a NAME="E7:99"/><b>then </b>
 <a href="chain_1.html#K10" title="CHAIN_1:func.10">del</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">C</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K11" title="CHAIN_1:func.11">0_</a> <font color="Maroon" title="c5">d'</font>,<font color="Maroon" title="c6">G</font>
 
<b>by </b><i><a class="ref" href="chain_1.html#T64" target="_self" title="CHAIN_1:th.64">Th64</a></i>;<br/>
<b>hence </b><a NAME="E8:99"/>
<font color="Maroon" title="c3">C</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  is    <a href="chain_1.html#M3" title="CHAIN_1:mode.3">Cycle</a> of <font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font>
 <b>by </b><i><a class="txt" href="chain_1.html#E2:99"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="chain_1.html#T66" target="_self" title="CHAIN_1:th.66">Th66</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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