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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="qc_lang1.html#NM6">QC-pred_symbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:30"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">b<sub>1</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>2</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>5</sub></font>(<font color="Olive">b<sub>1</sub></font>) iff 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="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> <a href="recdef_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="recdef_1.html#K1">.</a> <a href="cqc_lang.html#K9">VERUM</a>  <a href="hidden.html#R1">=</a> 0 &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="subset_1.html#M2">Element</a> of  <a href="qc_lang1.html#K2">bound_QC-variables</a> <br/>for <font color="Olive">b<sub>7</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">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="recdef_1.html#K1">.</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="hidden.html#R1">=</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="recdef_1.html#K1">.</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="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>3</sub></font> <a href="recdef_1.html#K1">.</a> <font color="Olive">b<sub>4</sub></font>) &amp; <font color="Olive">b<sub>3</sub></font> <a href="recdef_1.html#K1">.</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="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>3</sub></font> <a href="recdef_1.html#K1">.</a> <font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="recdef_1.html#K1">.</a> <font color="Olive">b<sub>5</sub></font>) &amp; <font color="Olive">b<sub>3</sub></font> <a href="recdef_1.html#K1">.</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="hidden.html#R1">=</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="recdef_1.html#K1">.</a> <font color="Olive">b<sub>4</sub></font>) ) ) ) )
 
<b>by </b><i><a class="ref" href="cqc_sim1.html#D5" target="_self">Def5</a></i>;<br/>
<b>thus </b><a NAME="E2:30"/>
<font color="Maroon">H<sub>5</sub></font>(<font color="Maroon">c<sub>3</sub></font> <a href="cqc_lang.html#K8">!</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>)
 <b>from </b><i><a class="ref" href="cqc_lang.html#S6">CQC_LANG:sch 6</a>(<a class="txt" href="cqc_sim1.html#E1:30"><i><font color="Green">E20</font></i></a>);</i><br/>


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