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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="domain_1.html#K4">]</a></span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> or <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> ) </span>}</span> 
 ;<br/><a NAME="E2:21_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="domain_1.html#K4">]</a></span> &amp; ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> or <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> )
 ;<br/><b>hence </b><a NAME="E3:21_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span>,<span class="p2"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span>,<span class="p2"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span></span><a href="zfmisc_1.html#K3">:]</a></span>
 <b>by </b><i><a class="ref" href="mcart_1.html#T73">MCART_1:73</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:21"/>
<span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span><a href="domain_1.html#K4">]</a></span> where B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a>, B is   <a href="nat_1.html#NM1">Nat</a> : ( ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> or <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span> ) </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><span class="p2"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span>,<span class="p2"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span>,<span class="p2"><a href="domain_1.html#K8">{</a><span class="default">1,2,3</span><a href="domain_1.html#K8">}</a></span></span><a href="zfmisc_1.html#K3">:]</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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