<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>

<a NAME="E1:29"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is    <a href="subset_1.html#M1">Element</a> of  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 
<b>by </b><i><a class="ref" href="zf_lang.html#D9" target="_self">Def9</a></i>;<br/>
<b>assume </b><a NAME="E2:29"/><i><font color="Green">E17</font></i>: 
( not <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#NR1" target="_self">is_equality</a>  &amp; not <font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#NR2" target="_self">is_membership</a>  &amp; not <font color="Maroon">c<sub>1</sub></font> is <a href="zf_lang.html#V4" target="_self">negative</a> &amp; not <font color="Maroon">c<sub>1</sub></font> is <a href="zf_lang.html#V5" target="_self">conjunctive</a> &amp; not <font color="Maroon">c<sub>1</sub></font> is <a href="zf_lang.html#V6" target="_self">universal</a> )
 ;<br/>

<a NAME="E3:29"/><i><font color="Green">E18</font></i>: 
<a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> is  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_1"><b>proof </b></a><div class="add">

<a NAME="E1:29_1"/><i><font color="Green">E19</font></i>: 
<span class="p1">(<span class="default"><a href="zf_lang.html#K2" target="_self">x.</a> 0</span>)</span> <a href="zf_lang.html#K4" target="_self">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" target="_self">x.</a> 1</span>)</span> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 
<b>by </b><i><a class="ref" href="zf_lang.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E2:29_1"/>
<span class="p1">(<span class="default"><a href="zf_lang.html#K2" target="_self">x.</a> 0</span>)</span> <a href="zf_lang.html#K4" target="_self">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" target="_self">x.</a> 1</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="zf_lang.html#E2:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="zf_lang.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E3:29_1"/><b>then </b>
not <span class="p1">(<span class="default"><a href="zf_lang.html#K2" target="_self">x.</a> 0</span>)</span> <a href="zf_lang.html#K4" target="_self">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" target="_self">x.</a> 1</span>)</span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:29_1"/>
<a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> is  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> 
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:29_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:29_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:29_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 ;<br/><b>hence </b><a NAME="E3:29_2"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> 
 <b>by </b><i><a class="ref" href="zf_lang.html#D8" target="_self">Def8</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><a NAME="E1:29_3"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K4" target="_self">'='</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 <b>by </b><i><a class="ref" href="zf_lang.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E2:29_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K4" target="_self">'='</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="zf_lang.html#D10" target="_self">Def10</a></i>;<br/><a NAME="E3:29_3"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K4" target="_self">'='</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:29_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K4" target="_self">'='</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:29_3"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E5:29_3"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 <b>by </b><i><a class="ref" href="zf_lang.html#D8" target="_self">Def8</a></i>;<br/><a NAME="E6:29_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="zf_lang.html#D11" target="_self">Def11</a></i>;<br/><a NAME="E7:29_3"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E8:29_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="zf_lang.html#E5:29_3"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:29_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:29_4"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 ;<br/><a NAME="E3:29_4"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="zf_lang.html#K6" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 <b>by </b><i><a class="ref" href="zf_lang.html#D8" target="_self">Def8</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="zf_lang.html#NM2">ZF-formula</a> <b>by </b><i><a class="txt" href="zf_lang.html#E2:29_4"><i><font color="Green">E22</font></i></a>, <a class="ref" href="zf_lang.html#D9" target="_self">Def9</a></i>;<br/><a NAME="E5:29_4"/>
 <a href="zf_lang.html#K6" target="_self">'not'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="zf_lang.html#D12" target="_self">Def12</a></i>;<br/><a NAME="E6:29_4"/><b>then </b>
not  <a href="zf_lang.html#K6" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:29_4"/>
 <a href="zf_lang.html#K6" target="_self">'not'</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:29_4"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="29_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:29_5"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> )
 ;<br/><a NAME="E2:29_5"/><b>then </b><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a>  )
 ;<br/><a NAME="E3:29_5"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 <b>by </b><i><a class="ref" href="zf_lang.html#D8" target="_self">Def8</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="zf_lang.html#NM2">ZF-formula</a> <b>by </b><i><a class="txt" href="zf_lang.html#E2:29_5"><i><font color="Green">E23</font></i></a>, <a class="ref" href="zf_lang.html#D9" target="_self">Def9</a></i>;<br/><a NAME="E5:29_5"/>
<font color="Maroon">c<sub>4</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="zf_lang.html#D13" target="_self">Def13</a></i>;<br/><a NAME="E6:29_5"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:29_5"/>
<font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K7" target="_self">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:29_5"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="29_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:29_6"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:29_6"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 ;<br/><a NAME="E3:29_6"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="zf_lang.html#K9" target="_self">WFF</a> 
 <b>by </b><i><a class="ref" href="zf_lang.html#D8" target="_self">Def8</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="zf_lang.html#NM2">ZF-formula</a> <b>by </b><i><a class="txt" href="zf_lang.html#E2:29_6"><i><font color="Green">E23</font></i></a>, <a class="ref" href="zf_lang.html#D9" target="_self">Def9</a></i>;<br/><a NAME="E5:29_6"/>
 <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="zf_lang.html#E2:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="zf_lang.html#D14" target="_self">Def14</a></i>;<br/><a NAME="E6:29_6"/><b>then </b>
not  <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:29_6"/>
 <a href="zf_lang.html#K8" target="_self">All</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="zf_lang.html#E3:29_6"><i><font color="Green">E24</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<a NAME="E9:29"/><b>then </b>
 <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="tarski.html#R1">c=</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="zf_lang.html#E3:29"><i><font color="Green">E18</font></i></a>, <a class="txt" href="zf_lang.html#E4:29"><i><font color="Green">E19</font></i></a>, <a class="txt" href="zf_lang.html#E5:29"><i><font color="Green">E20</font></i></a>, <a class="txt" href="zf_lang.html#E6:29"><i><font color="Green">E21</font></i></a>, <a class="txt" href="zf_lang.html#E7:29"><i><font color="Green">E22</font></i></a>, <a class="ref" href="zf_lang.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E10:29"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <a href="zf_lang.html#K9" target="_self">WFF</a>  <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="zf_lang.html#E1:29"><i><font color="Green">E16</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E11:29"/><b>then </b>
( not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E12:29"/>
contradiction
 ;<br/>


</div>
