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

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>( non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ,   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="msualg_1.html#L1">ManySortedSign</a>  = <font color="Maroon">a<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">a<sub>2</sub></font>,<font color="Maroon">a<sub>3</sub></font>);<br/>
<a NAME="E1:13_1"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">S</font> being non <a href="struct_0.html#V3">empty</a> <a href="msualg_1.html#V1">strict</a> non <a href="msualg_1.html#V2">void</a> <a href="circcomb.html#V1">unsplit</a> <a href="circcomb.html#V2">gate`1=arity</a> <a href="circcomb.html#V3">gate`2isBoolean</a>  <a href="msualg_1.html#L1">ManySortedSign</a> <br/> for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a> <br/> for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>,<font color="Olive">x</font>,<font color="Olive">n</font>) is <a href="circcomb.html#V1">unsplit</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>,<font color="Olive">x</font>,<font color="Olive">n</font>) is <a href="circcomb.html#V2">gate`1=arity</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>,<font color="Olive">x</font>,<font color="Olive">n</font>) is <a href="circcomb.html#V3">gate`2isBoolean</a> &amp; not <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>,<font color="Olive">x</font>,<font color="Olive">n</font>) is <a href="msualg_1.html#V2">void</a> &amp; not <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>,<font color="Olive">x</font>,<font color="Olive">n</font>) is <a href="struct_0.html#V3">empty</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>,<font color="Olive">x</font>,<font color="Olive">n</font>) is <a href="msualg_1.html#V1">strict</a> )
 
;<br/>
<b>thus </b><a NAME="E2:13_1"/>
 ex <font color="Olive">S</font> being non <a href="struct_0.html#V3">empty</a> <a href="msualg_1.html#V1">strict</a> non <a href="msualg_1.html#V2">void</a> <a href="circcomb.html#V1">unsplit</a> <a href="circcomb.html#V2">gate`1=arity</a> <a href="circcomb.html#V3">gate`2isBoolean</a>  <a href="msualg_1.html#L1">ManySortedSign</a>  ex <font color="Olive">f</font>, <font color="Olive">h</font> being   <a href="pboole.html#M1">ManySortedSet</a> of  <a href="numbers.html#K5">NAT</a>  st <br/>( <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>5</sub></font>() &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive">h</font> <a href="funct_1.html#K1">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>() &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">S</font> being non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> <br/> for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">S</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">h</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> holds <br/>( <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">S</font>,<font color="Olive">x</font>,<font color="Olive">n</font>) &amp; <font color="Olive">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">n</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive">x</font>,<font color="Olive">n</font>) ) ) )
 <b>from </b><i><a class="ref" href="circcmb2.html#S7" target="_self">CIRCCMB2:sch 7</a>(, );</i><br/>


</div>
