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<b>set </b><font color="Maroon" title="c1">A</font> = <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>) where <font color="Olive" title="b1">u1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>] </span>}</span> ;<br/>
<b>set </b><font color="Maroon" title="c2">B</font> = <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>) where <font color="Olive" title="b1">u2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>] </span>}</span> ;<br/>
<a NAME="E1:4_1"/><i><font color="Green" title="E2">A2</font></i>: 
for <font color="Olive" title="b1">u</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive" title="b2">v</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font>] holds <br/><font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font>]
 
<b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<b>thus </b><a NAME="E2:4_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>) where <font color="Olive" title="b1">u1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>] </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>) where <font color="Olive" title="b1">u2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>] </span>}</span> 
 <b>from </b><i><a class="ref" href="fraenkel.html#S2" target="_self" title="FRAENKEL:sch.2">FRAENKEL:sch 2</a>(<a class="txt" href="#E1:4_1"><i><font color="Green" title="E2">A2</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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>) where <font color="Olive" title="b1">u2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>] </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>) where <font color="Olive" title="b1">u1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>] </span>}</span> </span><br/>

<a NAME="E3:4_1"/><i><font color="Green" title="E3">A3</font></i>: 
for <font color="Olive" title="b1">u</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive" title="b2">v</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font>] holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font>]
 
<b>by </b><i><a class="txt" href="#E1:4"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<b>thus </b><a NAME="E4:4_1"/>
<span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>) where <font color="Olive" title="b1">u2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">u2</font>,<font color="Olive" title="b2">v2</font>] </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>) where <font color="Olive" title="b1">u1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">v1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font>] </span>}</span> 
 <b>from </b><i><a class="ref" href="fraenkel.html#S2" target="_self" title="FRAENKEL:sch.2">FRAENKEL:sch 2</a>(<a class="txt" href="#E3:4_1"><i><font color="Green" title="E3">A3</font></i></a>);</i> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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