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<div><div><a NAME="S3"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: PROOFS_1:sch 3</font></span><br/></a><span class="lab"><font color="Green" title="E3">ProofInduction</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="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a>, <font color="Maroon">P<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ] } :<br/><div class="add"><a NAME="E3:98"/>
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>() <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b1">a</font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">a</font>]
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:98"/><span class="lab"><font color="Green" title="E37">A1</font></span>: 
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">a</font>]
 <span class="kw">and </span><br/><a NAME="E2:98"/><span class="lab"><font color="Green" title="E38">A2</font></span>: 
 for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">a</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>() &amp; (  for <font color="Olive" title="b3">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b3">b</font>] ) holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b2">a</font>]
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