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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_1_2"/><i><font color="Green">E1</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> iff <font color="Olive">b<sub>1</sub></font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a> )
 <b>and </b><br/><a NAME="E2:1_1_2"/><i><font color="Green">E2</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Olive">b<sub>1</sub></font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a> )
 ;<br/>

<a NAME="E3:1_1_2"/><i><font color="Green">E3</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></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="E1:1_1_2_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:1_1_2_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a>
 
<b>by </b><i><a class="txt" href="csspace.html#E1:1_1_2"><i><font color="Green">E1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:1_1_2_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="csspace.html#E2:1_1_2"><i><font color="Green">E2</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></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="E1:1_1_2_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:1_1_2_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a>
 
<b>by </b><i><a class="txt" href="csspace.html#E2:1_1_2"><i><font color="Green">E2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:1_1_2_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="csspace.html#E1:1_1_2"><i><font color="Green">E1</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:1_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="csspace.html#E3:1_1_2"><i><font color="Green">E3</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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