<?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" title="STRUCT_0:attr.3">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a>  = $1 <a href="circcomb.html#K3" title="CIRCCOMB:func.3">+*</a> <font color="Maroon">F<sub>2</sub></font>($2,$3);<br/>
<a NAME="E1:13_1"/><i><font color="Green" title="E5">A2</font></i>: 
for <font color="Olive" title="b1">S</font> being non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="circcomb.html#V1" title="CIRCCOMB:attr.1">unsplit</a> <a href="circcomb.html#V2" title="CIRCCOMB:attr.2">gate`1=arity</a> <a href="circcomb.html#V3" title="CIRCCOMB:attr.3">gate`2isBoolean</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/> for <font color="Olive" title="b2">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b3">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/> ( <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">n</font>) is <a href="circcomb.html#V1" title="CIRCCOMB:attr.1">unsplit</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">n</font>) is <a href="circcomb.html#V2" title="CIRCCOMB:attr.2">gate`1=arity</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">n</font>) is <a href="circcomb.html#V3" title="CIRCCOMB:attr.3">gate`2isBoolean</a> &amp; not <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">n</font>) is <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> &amp; not <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">n</font>) is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> &amp; <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">S</font>,<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">n</font>) is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> )
 
;<br/>
<b>thus </b><a NAME="E2:13_1"/>
 ex <font color="Olive" title="b1">S</font> being non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> non <a href="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a> <a href="circcomb.html#V1" title="CIRCCOMB:attr.1">unsplit</a> <a href="circcomb.html#V2" title="CIRCCOMB:attr.2">gate`1=arity</a> <a href="circcomb.html#V3" title="CIRCCOMB:attr.3">gate`2isBoolean</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a>  ex <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">h</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() &amp; <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Olive" title="b3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>() &amp; ( for <font color="Olive" title="b4">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b5">S</font> being non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/> for <font color="Olive" title="b6">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b5">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font> &amp; <font color="Olive" title="b6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font> holds <br/>( <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b5">S</font>,<font color="Olive" title="b6">x</font>,<font color="Olive" title="b4">n</font>) &amp; <font color="Olive" title="b3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive" title="b6">x</font>,<font color="Olive" title="b4">n</font>) ) ) )
 <b>from </b><i><a class="ref" href="circcmb2.html#S7" target="_self" title="CIRCCMB2:sch.7">CIRCCMB2:sch 7</a>(<a class="txt" href="circcmb2.html#E1:13"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="circcmb2.html#E1:13_1"><i><font color="Green" title="E5">A2</font></i></a>);</i><br/>


</div>
