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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">zero</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="chain_1.html#M1" target="_self">Grating</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="chain_1.html#NM4">Chain</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="chain_1.html#NM3">Cell</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><a NAME="E1:90_1"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K5">\+\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K5">\+\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T112">XBOOLE_1:112</a></i>;<br/><a NAME="E2:90_1"/>
( ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K11" target="_self">del</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> implies ( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; not  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K5">\+\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> is <a href="abian.html#V1">even</a> ) ) &amp; ( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; not  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K5">\+\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> is <a href="abian.html#V1">even</a> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K11" target="_self">del</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> ) &amp; ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>4</sub></font> implies ( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; not  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) ) &amp; ( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; not  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>4</sub></font> ) &amp; ( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>5</sub></font> implies ( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; not  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> is <a href="abian.html#V1">even</a> ) ) &amp; ( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; not  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="chain_1.html#K10" target="_self">star</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> is <a href="abian.html#V1">even</a> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>5</sub></font> ) )
 <b>by </b><i><a class="ref" href="chain_1.html#T52" target="_self">Th52</a></i>;<br/><b>hence </b><a NAME="E3:90_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K11" target="_self">del</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> iff <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="chain_1.html#K8" target="_self">+</a> <span class="p1">(<span class="default"><a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="chain_1.html#E1:90_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="chain_1.html#T9" target="_self">Th9</a>, <a class="ref" href="xboole_0.html#T1">XBOOLE_0:1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:90"/>
 <a href="chain_1.html#K11" target="_self">del</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K8" target="_self">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="chain_1.html#K8" target="_self">+</a> <span class="p1">(<span class="default"><a href="chain_1.html#K11" target="_self">del</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="subset_1.html#T8">SUBSET_1:8</a></i>;<br/>


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