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<div><div><a NAME="S12"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: FRAENKEL:sch 12</font></span><br/></a><span class="lab"><font color="Green" title="E12">Gen199A</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>2</sub></font>() <span class="kw">-&gt; </span>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>3</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> , <font color="Maroon">P<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ], <font color="Maroon">P<sub>2</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] } :<br/><div class="add"><a NAME="E2:15"/>
 for <font color="Olive" title="b1">st1</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">st1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b2">s1</font>,<font color="Olive" title="b3">t1</font>) where <font color="Olive" title="b2">s1</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="b3">t1</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="b2">s1</font>,<font color="Olive" title="b3">t1</font>] </span> } </span>  holds <br/><font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">st1</font>]
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:15"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
 for <font color="Olive" title="b1">s</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">t</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">s</font>,<font color="Olive" title="b2">t</font>] holds <br/><font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s</font>,<font color="Olive" title="b2">t</font>)]
 </div></div></div>
