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<b>let </b><font color="Maroon">v1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="zf_lang.html#K1">VAR</a> ;<br/>

<b>thus </b><a NAME="E1:15"/>
 <a href="zf_fund1.html#K5" target="_self">code</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v1</font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">v1</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">p</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:15_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K5" target="_self">code</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v1</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">v2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="zf_lang.html#K1">VAR</a> <b> such that </b><br/><a NAME="E3:15_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">v2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v1</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">v2</font> )
 <b>by </b><i/>;<br/>
<a NAME="E4:15_1"/>
<font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">v1</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">p</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:15"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">v1</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E3:15"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">v1</font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:15"/>
<font color="Maroon">v1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v1</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K5" target="_self">code</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v1</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, </i>;<br/>


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