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<div><div><a NAME="S2"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: GRZLOG_1:sch 2</font></span><br/></a><span class="lab"><font color="Green" title="E2">UnOpCongr</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>2</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Maroon">F<sub>3</sub></font>() <span class="kw">-&gt; </span>  <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Maroon">F<sub>1</sub></font>() } :<br/><div class="add"><a NAME="E2:83"/>
 ex <font color="Olive" title="b1">f</font> being   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> st <br/> for <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds  <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Olive" title="b2">x</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<font color="Maroon">F<sub>3</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b2">x</font>))
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:83"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()  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">y</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>3</sub></font>() holds <br/><span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">x</font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b2">y</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>3</sub></font>()
 </div></div></div>
