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<span class="kw">let </span><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:()"><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">d</font> holds <br/> (  <a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d</font>,<font color="Olive" title="b1">G</font>)</span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp;  <a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d</font>,<font color="Olive" title="b1">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )</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">d</font>; <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#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font>)</span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp;  <a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )</span><br/>



<a NAME="E1:80"/>
 <a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font>)</span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E2:80"/>
(  <a href="chain_1.html#K6" title="CHAIN_1:func.6">Omega</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font>)</span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  &amp;  <a href="chain_1.html#K5" title="CHAIN_1:func.5">0_</a> (<font color="Maroon" title="c1">d</font>,<font color="Maroon" title="c2">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 ; <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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