<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="margrel1.html#K1">--&gt;</a> <a href="margrel1.html#K8">TRUE</a> ;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1">Nat</a>,  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">a<sub>1</sub></font>,  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">a<sub>1</sub></font>) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  = <font color="Maroon">a<sub>3</sub></font> <a href="valuat_1.html#K9" target="_self">'in'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="valuat_1.html#K11" target="_self">.</a> <font color="Maroon">a<sub>2</sub></font></span>)</span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  =  <a href="valuat_1.html#K5" target="_self">'not'</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a> ,   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  = <font color="Maroon">a<sub>1</sub></font> <a href="valuat_1.html#K6" target="_self">'&amp;'</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>4</sub></font>(  <a href="qc_lang1.html#NM3">bound_QC-variable</a>,   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a> ) <b>-&gt; </b>   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  =  <a href="valuat_1.html#K7" target="_self">FOR_ALL</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">a<sub>2</sub></font>;<br/>
<b>thus </b><a NAME="E1:21_1_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a> ex <font color="Olive">b<sub>2</sub></font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> , <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <a href="cqc_lang.html#K9">VERUM</a>  <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="margrel1.html#K1">--&gt;</a> <a href="margrel1.html#K8">TRUE</a>  &amp; ( for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> <br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a><br/>for <font color="Olive">b<sub>6</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>7</sub></font> being  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Olive">b<sub>6</sub></font><br/>for <font color="Olive">b<sub>8</sub></font> being  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">b<sub>6</sub></font> holds <br/>( <font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>8</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">b<sub>7</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>8</sub></font>,<font color="Olive">b<sub>7</sub></font>) &amp; <font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>3</sub></font>) &amp; <font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>4</sub></font>) &amp; <font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>3</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>3</sub></font>) ) ) ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  st ex <font color="Olive">b<sub>3</sub></font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> , <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <a href="cqc_lang.html#K9">VERUM</a>  <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="margrel1.html#K1">--&gt;</a> <a href="margrel1.html#K8">TRUE</a>  &amp; ( for <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> <br/>for <font color="Olive">b<sub>6</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a><br/>for <font color="Olive">b<sub>7</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>8</sub></font> being  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Olive">b<sub>7</sub></font><br/>for <font color="Olive">b<sub>9</sub></font> being  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">b<sub>7</sub></font> holds <br/>( <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>9</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">b<sub>8</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>8</sub></font>) &amp; <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>4</sub></font>) &amp; <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">b<sub>5</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>5</sub></font>) &amp; <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>4</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>4</sub></font>) ) ) ) &amp; ex <font color="Olive">b<sub>3</sub></font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> , <a href="fraenkel.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<a href="margrel1.html#K6">BOOLEAN</a>  st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <a href="cqc_lang.html#K9">VERUM</a>  <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K2" target="_self">Valuations_in</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="margrel1.html#K1">--&gt;</a> <a href="margrel1.html#K8">TRUE</a>  &amp; ( for <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="cqc_lang.html#K7">CQC-WFF</a> <br/>for <font color="Olive">b<sub>6</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a><br/>for <font color="Olive">b<sub>7</sub></font> being  <a href="nat_1.html#NM1">Nat</a><br/>for <font color="Olive">b<sub>8</sub></font> being  <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Olive">b<sub>7</sub></font><br/>for <font color="Olive">b<sub>9</sub></font> being  <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Olive">b<sub>7</sub></font> holds <br/>( <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>9</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Olive">b<sub>8</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>7</sub></font>,<font color="Olive">b<sub>9</sub></font>,<font color="Olive">b<sub>8</sub></font>) &amp; <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K10">'not'</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>4</sub></font>) &amp; <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="cqc_lang.html#K11">'&amp;'</a> <font color="Olive">b<sub>5</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>5</sub></font>) &amp; <font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <span class="p1">(<span class="default"><a href="cqc_lang.html#K15">All</a> <font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>4</sub></font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">H<sub>4</sub></font>(<font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="valuat_1.html#K10" target="_self">.</a> <font color="Olive">b<sub>4</sub></font>) ) ) ) holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <font color="Olive">b<sub>2</sub></font> ) )
 <b>from </b><i><a class="ref" href="cqc_lang.html#S4">CQC_LANG:sch 4</a>();</i><br/>


</div>
