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<a NAME="E1:25_1"/><i><font color="Green">E5</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  st ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] holds <br/><font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) holds <br/><span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>2</sub></font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="domain_1.html#S5" target="_self">DOMAIN_1:sch 5</a>();<br/></i>
<a NAME="E2:25_1"/><i><font color="Green">E6</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  st ( for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> st <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>2</sub></font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] ) holds <br/><span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>2</sub></font>] </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>2</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Olive">b<sub>1</sub></font> : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="domain_1.html#S5" target="_self">DOMAIN_1:sch 5</a>();<br/></i>
<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E3:25_1"/><i><font color="Green">E7</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] iff <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 ;<br/>

<b>hence </b><a NAME="E4:25_1"/>
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span> 
 <b>by </b><i><a class="txt" href="domain_1.html#E1:25_1"><i><font color="Green">E5</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E5:25_1"/>
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span> 
 <b>by </b><i><a class="txt" href="domain_1.html#E2:25_1"><i><font color="Green">E6</font></i></a>, <a class="txt" href="domain_1.html#E3:25_1"><i><font color="Green">E7</font></i></a></i>;<br/>


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