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<span class="kw">let </span><font color="Maroon" title="c1">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">d</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">G</font> being    <a href="chain_1.html#M1" title="CHAIN_1:mode.1">Grating</a> of <font color="Olive" title="b1">d</font><br/>  for <font color="Olive" title="b3">A</font> being   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</a> of <font color="Maroon" title="c1">k</font>,<font color="Olive" title="b2">G</font><br/>  for <font color="Olive" title="b4">B</font> being   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</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="Olive" title="b2">G</font> holds <br/> ( <font color="Olive" title="b4">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Olive" title="b3">A</font> iff <font color="Olive" title="b3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">d</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="c2">d</font><br/>  for <font color="Olive" title="b2">A</font> being   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</a> of <font color="Maroon" title="c1">k</font>,<font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">B</font> being   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</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="Olive" title="b1">G</font> holds <br/> ( <font color="Olive" title="b3">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Olive" title="b2">A</font> iff <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">B</font> )</span><br/><span class="kw">let </span><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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</a> of <font color="Maroon" title="c1">k</font>,<font color="Maroon" title="c3">G</font><br/>  for <font color="Olive" title="b2">B</font> being   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</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> holds <br/> ( <font color="Olive" title="b2">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Olive" title="b1">A</font> iff <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font> be   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</a> of <font color="Maroon" title="c1">k</font>,<font color="Maroon" title="c3">G</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">B</font> being   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</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> holds <br/> ( <font color="Olive" title="b1">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Maroon" title="c4">A</font> iff <font color="Maroon" title="c4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">B</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">B</font> be   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Maroon" title="c4">A</font> iff <font color="Maroon" title="c4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">B</font> )</span><br/>









<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ] <span class="kw">means </span><font color="Maroon" title="c4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> $1;<br/>
<a NAME="E1:74"/><span class="lab"><font color="Green" title="E49">A1</font></span>: 
 <a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">B9</font> where <font color="Olive" title="b1">B9</font> is   <a href="chain_1.html#NM3" title="CHAIN_1:NM.3">Cell</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> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">B9</font>] </span> } </span> 
 
;<br/>
<span class="kw">thus </span><a NAME="E2:74"/>
( <font color="Maroon" title="c5">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="chain_1.html#K9" title="CHAIN_1:func.9">star</a> <font color="Maroon" title="c4">A</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c5">B</font>] )
 <span class="kw">from</span> <span class="lab"><a class="ref" href="lmod_7.html#S7" onmouseover="rs('lmod_7/S7')" onmouseout="rh()">LMOD_7:sch 7</a>(<a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E49">A1</font></span></a>);</span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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