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<a NAME="E1:25_1"/><i><font color="Green" title="E5">A1</font></i>: 
for <font color="Olive" title="b1">X1</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st ( for <font color="Olive" title="b2">x1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X1</font>  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">x1</font>] holds <br/><font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b2">x1</font>] ) holds <br/><span class="p1">{<span class="default"> <font color="Olive" title="b2">y1</font> where <font color="Olive" title="b2">y1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X1</font> : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">y1</font>] </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">z1</font> where <font color="Olive" title="b2">z1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X1</font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b2">z1</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="domain_1.html#S5" target="_self" title="DOMAIN_1:sch.5">DOMAIN_1:sch 5</a>();<br/></i>
<a NAME="E2:25_1"/><i><font color="Green" title="E6">A2</font></i>: 
for <font color="Olive" title="b1">X1</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st ( for <font color="Olive" title="b2">x1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X1</font>  st <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b2">x1</font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">x1</font>] ) holds <br/><span class="p1">{<span class="default"> <font color="Olive" title="b2">y1</font> where <font color="Olive" title="b2">y1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X1</font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b2">y1</font>] </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b2">z1</font> where <font color="Olive" title="b2">z1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X1</font> : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">z1</font>] </span>}</span> 
 
<b>from </b><i><a class="ref" href="domain_1.html#S5" target="_self" title="DOMAIN_1:sch.5">DOMAIN_1:sch 5</a>();<br/></i>
<b>let </b><font color="Maroon" title="c1">X1</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E3:25_1"/><i><font color="Green" title="E7">A3</font></i>: 
for <font color="Olive" title="b1">x1</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> holds <br/> ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">x1</font>] iff <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">x1</font>] )
 ;<br/>

<b>hence </b><a NAME="E4:25_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y1</font> where <font color="Olive" title="b1">y1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">y1</font>] </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">z1</font> where <font color="Olive" title="b1">z1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">z1</font>] </span>}</span> 
 <b>by </b><i><a class="txt" href="domain_1.html#E1:25_1"><i><font color="Green" title="E5">A1</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E5:25_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y1</font> where <font color="Olive" title="b1">y1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">y1</font>] </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">z1</font> where <font color="Olive" title="b1">z1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X1</font> : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">z1</font>] </span>}</span> 
 <b>by </b><i><a class="txt" href="domain_1.html#E2:25_1"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="domain_1.html#E3:25_1"><i><font color="Green" title="E7">A3</font></i></a></i>;<br/>


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