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<span class="kw">let </span><font color="Maroon" title="c1">d9</font> be    <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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">d9</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 holds   <a href="chain_1.html#K10" title="CHAIN_1:func.10">del</a> <span class="p1">(<span class="default"><a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Olive" title="b1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d9</font>,<font color="Olive" title="b1">G</font>)</span><br/><span class="kw">let </span><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">d9</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="chain_1.html#K10" title="CHAIN_1:func.10">del</a> <span class="p1">(<span class="default"><a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d9</font>,<font color="Maroon" title="c2">G</font>)</span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</a> of <font color="Maroon" title="c1">d9</font>,<font color="Maroon" title="c2">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="chain_1.html#K10" title="CHAIN_1:func.10">del</a> <span class="p1">(<span class="default"><a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font></span>)</span> iff <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d9</font>,<font color="Maroon" title="c2">G</font>) )</span><br/><a NAME="E1:83_1"/>
<span class="p1">(<span class="default"><a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>;<br/><a NAME="E2:83_1"/><span class="kw">then </span>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="chain_1.html#T54" target="_self" title="CHAIN_1:th.54">Th55</a></span>;<br/><span class="kw">hence </span><a NAME="E3:83_1"/>
( <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="chain_1.html#K10" title="CHAIN_1:func.10">del</a> <span class="p1">(<span class="default"><a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font></span>)</span> iff <font color="Maroon" title="c3">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d9</font>,<font color="Maroon" title="c2">G</font>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="chain_1.html#T51" target="_self" title="CHAIN_1:th.51">Th52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:83"/>
 <a href="chain_1.html#K10" title="CHAIN_1:func.10">del</a> <span class="p1">(<span class="default"><a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d9</font>,<font color="Maroon" title="c2">G</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T3" title="SUBSET_1:th.3">SUBSET_1:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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