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

<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be  non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font> implies for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="algspec1.html#R1" title="ALGSPEC1:pred.1">form_a_replacement_in</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S2</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E1:61"/><i><font color="Green" title="E46">A1</font></i>: 
<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="algspec1.html#R1" title="ALGSPEC1:pred.1">form_a_replacement_in</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S2</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c3">S</font> = <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>;<br/>
<b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> <a href="algspec1.html#R1" title="ALGSPEC1:pred.1">form_a_replacement_in</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S2</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> )</span><br/>

<b>assume </b><a NAME="E2:61"/><i><font color="Green" title="E47">A2</font></i>: 
<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> <a href="algspec1.html#R1" title="ALGSPEC1:pred.1">form_a_replacement_in</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S2</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span></span><br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>( non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>) <b>-&gt; </b> non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a>  = $1 <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>( non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>) <b>-&gt; </b>   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of $1 = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of $1 <a href="algspec1.html#K1" title="ALGSPEC1:func.1">-indexing</a> <font color="Maroon" title="c4">f</font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>( non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>) <b>-&gt; </b>   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of $1 = the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of $1 <a href="algspec1.html#K1" title="ALGSPEC1:func.1">-indexing</a> <font color="Maroon" title="c5">g</font>;<br/>
<a NAME="E3:61"/><i><font color="Green" title="E48">A3</font></i>: 
( <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="algspec1.html#T49" target="_self" title="ALGSPEC1:th.49">Th49</a>, <a class="ref" href="algspec1.html#T50" target="_self" title="ALGSPEC1:th.50">Th50</a></i>;<br/>
<a NAME="E4:61"/><b>then </b><i><font color="Green" title="E49">A4</font></i>: 
( <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> <a href="algspec1.html#R1" title="ALGSPEC1:pred.1">form_a_replacement_in</a> <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> <a href="algspec1.html#R1" title="ALGSPEC1:pred.1">form_a_replacement_in</a> <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="algspec1.html#T54" target="_self" title="ALGSPEC1:th.54">Th54</a></i>;<br/>
<a NAME="E5:61"/><i><font color="Green" title="E50">A5</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E6:61"/><b>then </b>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>)
 
<b>by </b><i><a class="ref" href="algspec1.html#T21" target="_self" title="ALGSPEC1:th.21">Th21</a></i>;<br/>
<a NAME="E7:61"/><b>then </b><i><font color="Green" title="E51">A6</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>)</span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>)</span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T26" title="RELAT_1:th.26">RELAT_1:26</a></i>;<br/>
<a NAME="E8:61"/><i><font color="Green" title="E52">A7</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="#E4:61"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="algspec1.html#D4" target="_self" title="ALGSPEC1:def.4">Def4</a></i>;<br/>
<a NAME="E9:61"/><i><font color="Green" title="E53">A8</font></i>: 
( the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E10:61"/><b>then </b>
<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>)
 
<b>by </b><i><a class="ref" href="algspec1.html#T21" target="_self" title="ALGSPEC1:th.21">Th21</a></i>;<br/>
<a NAME="E11:61"/><b>then </b><i><font color="Green" title="E54">A9</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>)</span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>)</span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T26" title="RELAT_1:th.26">RELAT_1:26</a></i>;<br/>
<a NAME="E12:61"/><i><font color="Green" title="E55">A10</font></i>: 
( the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>) &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="#E4:61"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="algspec1.html#D4" target="_self" title="ALGSPEC1:def.4">Def4</a></i>;<br/>
<a NAME="E13:61"/><i><font color="Green" title="E56">A11</font></i>: 
( the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E14:61"/><i><font color="Green" title="E57">A12</font></i>: 
( the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">g1</font> being    <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>), <font color="Maroon" title="c7">g2</font> being    <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>);<br/>
<a NAME="E16:61"/>
( <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>) &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="circcomb.html#K1" title="CIRCCOMB:func.1">+*</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="txt" href="#E9:61"><i><font color="Green" title="E53">A8</font></i></a>, <a class="ref" href="algspec1.html#T19" target="_self" title="ALGSPEC1:th.19">Th19</a>, <a class="ref" href="algspec1.html#T20" target="_self" title="ALGSPEC1:th.20">Th20</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c8">gg</font> = <font color="Maroon" title="c6">g1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c7">g2</font> as    <a href="algspec1.html#M1" title="ALGSPEC1:mode.1">rng-retract</a> of <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <b>by </b><i><a class="ref" href="algspec1.html#T28" target="_self" title="ALGSPEC1:th.28">Th28</a></i>;<br/>
<a NAME="E18:61"/><i><font color="Green" title="E58">A13</font></i>: 
( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="circcomb.html#K1" title="CIRCCOMB:func.1">+*</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="txt" href="#E5:61"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="algspec1.html#T19" target="_self" title="ALGSPEC1:th.19">Th19</a>, <a class="ref" href="algspec1.html#T20" target="_self" title="ALGSPEC1:th.20">Th20</a></i>;<br/>
<a NAME="E19:61"/><i><font color="Green" title="E59">A14</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> )
 
;<br/>
<a NAME="E20:61"/><i><font color="Green" title="E60">A15</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E21:61"/><i><font color="Green" title="E61">A16</font></i>: 
(  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">g1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>) &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">g2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>) )
 
<b>by </b><i><a class="ref" href="algspec1.html#T24" target="_self" title="ALGSPEC1:th.24">Th24</a></i>;<br/>
<a NAME="E22:61"/><i><font color="Green" title="E62">A17</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E23:61"/><i><font color="Green" title="E63">A18</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E24:61"/><i><font color="Green" title="E64">A19</font></i>: 
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font>
 
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="circcomb.html#D1" title="CIRCCOMB:def.1">CIRCCOMB:def 1</a></i>;<br/>
<i><font color="Green" title="E65">A20</font></i>: the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) = 
<span class="p1">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c8">gg</font>
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="algspec1.html#T39" target="_self" title="ALGSPEC1:th.39">Th39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="circcomb.html#K1" title="CIRCCOMB:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c8">gg</font>
<b>by </b><i><a class="txt" href="#E14:61"><i><font color="Green" title="E57">A12</font></i></a>, <a class="txt" href="#E18:61"><i><font color="Green" title="E58">A13</font></i></a>, <a class="txt" href="#E19:61"><i><font color="Green" title="E59">A14</font></i></a>, <a class="txt" href="#E20:61"><i><font color="Green" title="E60">A15</font></i></a>, <a class="ref" href="funct_4.html#T73" title="FUNCT_4:th.73">FUNCT_4:73</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">g2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E18:61"><i><font color="Green" title="E58">A13</font></i></a>, <a class="txt" href="#E21:61"><i><font color="Green" title="E61">A16</font></i></a>, <a class="txt" href="#E22:61"><i><font color="Green" title="E62">A17</font></i></a>, <a class="txt" href="#E23:61"><i><font color="Green" title="E63">A18</font></i></a>, <a class="txt" href="#E24:61"><i><font color="Green" title="E64">A19</font></i></a>, <a class="ref" href="algspec1.html#T4" target="_self" title="ALGSPEC1:th.4">Th4</a>, <a class="ref" href="funct_4.html#T73" title="FUNCT_4:th.73">FUNCT_4:73</a></i>
<br/>.= 
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="pboole.html#K7" title="PBOOLE:func.7">*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">g2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="#E3:61"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="algspec1.html#T39" target="_self" title="ALGSPEC1:th.39">Th39</a>, <a class="ref" href="algspec1.html#T54" target="_self" title="ALGSPEC1:th.54">Th54</a></i>
<br/>.= 
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="#E3:61"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="algspec1.html#T39" target="_self" title="ALGSPEC1:th.39">Th39</a>, <a class="ref" href="algspec1.html#T54" target="_self" title="ALGSPEC1:th.54">Th54</a></i>
;<br/>
<b>reconsider </b><font color="Maroon" title="c9">FS</font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) <b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="algspec1.html#T37" target="_self" title="ALGSPEC1:th.37">Th37</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">F1</font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font>) as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="#E3:61"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="algspec1.html#T37" target="_self" title="ALGSPEC1:th.37">Th37</a>, <a class="ref" href="algspec1.html#T54" target="_self" title="ALGSPEC1:th.54">Th54</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">F2</font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c2">S2</font>) as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) <b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="#E3:61"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="algspec1.html#T37" target="_self" title="ALGSPEC1:th.37">Th37</a>, <a class="ref" href="algspec1.html#T54" target="_self" title="ALGSPEC1:th.54">Th54</a></i>;<br/>
<a NAME="E29:61"/>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font>
 
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="circcomb.html#D1" title="CIRCCOMB:def.1">CIRCCOMB:def 1</a></i>;<br/>
<a NAME="E30:61"/><b>then </b>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font>
 
<b>by </b><i><a class="txt" href="#E13:61"><i><font color="Green" title="E56">A11</font></i></a>, <a class="ref" href="funct_4.html#T31" title="FUNCT_4:th.31">FUNCT_4:31</a></i>;<br/>
<a NAME="E31:61"/><b>then </b><i><font color="Green" title="E66">A21</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T26" title="RELAT_1:th.26">RELAT_1:26</a></i>;<br/>
<a NAME="E32:61"/><i><font color="Green" title="E67">A22</font></i>: 
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  )
 
;<br/>
<a NAME="E33:61"/><i><font color="Green" title="E68">A23</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E31:61"><i><font color="Green" title="E66">A21</font></i></a>, <a class="ref" href="xboole_1.html#T13" title="XBOOLE_1:th.13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E34:61"/>
( <font color="Maroon" title="c10">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">FS</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c11">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">FS</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="txt" href="#E5:61"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="algspec1.html#T18" target="_self" title="ALGSPEC1:th.18">Th18</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E35:61"/><b>then </b>
( <font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a>  <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c9">FS</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a>  &amp; <font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a>  <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c9">FS</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a>  )
 
<b>by </b><i><a class="ref" href="algspec1.html#T5" target="_self" title="ALGSPEC1:th.5">Th5</a>, <a class="ref" href="relat_1.html#T88" title="RELAT_1:th.88">RELAT_1:88</a></i>;<br/>
<a NAME="E36:61"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">FS</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T30" title="FUNCT_4:th.30">FUNCT_4:30</a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E37:61"/><b>then </b><i><font color="Green" title="E69">A24</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">FS</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E38:61"/><i><font color="Green" title="E70">A25</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E39:61"/><b>then </b>
(  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">FS</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E33:61"><i><font color="Green" title="E68">A23</font></i></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E40:61"/><b>then </b><i><font color="Green" title="E71">A26</font></i>: 
<span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">FS</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E41:61"/><i><font color="Green" title="E72">A27</font></i>: 
<font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a>  <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> 
 
<b>by </b><i><a class="ref" href="algspec1.html#T20" target="_self" title="ALGSPEC1:th.20">Th20</a>, <a class="ref" href="algspec1.html#T6" target="_self" title="ALGSPEC1:th.6">Th6</a></i>;<br/>
<a NAME="E42:61"/><i><font color="Green" title="E73">A28</font></i>: 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font>
 
<b>by </b><i><a class="txt" href="#E1:61"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="circcomb.html#D1" title="CIRCCOMB:def.1">CIRCCOMB:def 1</a></i>;<br/>
<a NAME="E43:61"/><i><font color="Green" title="E74">A29</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">FS</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c8">gg</font>
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="algspec1.html#T38" target="_self" title="ALGSPEC1:th.38">Th38</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c8">gg</font>
<b>by </b><i><a class="txt" href="#E37:61"><i><font color="Green" title="E69">A24</font></i></a>, <a class="txt" href="#E40:61"><i><font color="Green" title="E71">A26</font></i></a>, <a class="ref" href="algspec1.html#T2" target="_self" title="ALGSPEC1:th.2">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c8">gg</font>
<b>by </b><i><a class="txt" href="#E13:61"><i><font color="Green" title="E56">A11</font></i></a>, <a class="txt" href="#E18:61"><i><font color="Green" title="E58">A13</font></i></a>, <a class="txt" href="#E32:61"><i><font color="Green" title="E67">A22</font></i></a>, <a class="txt" href="#E38:61"><i><font color="Green" title="E70">A25</font></i></a>, <a class="ref" href="algspec1.html#T6" target="_self" title="ALGSPEC1:th.6">Th6</a>, <a class="ref" href="funct_4.html#T73" title="FUNCT_4:th.73">FUNCT_4:73</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c6">g1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">g2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E21:61"><i><font color="Green" title="E61">A16</font></i></a>, <a class="txt" href="#E22:61"><i><font color="Green" title="E62">A17</font></i></a>, <a class="txt" href="#E41:61"><i><font color="Green" title="E72">A27</font></i></a>, <a class="txt" href="#E42:61"><i><font color="Green" title="E73">A28</font></i></a>, <a class="txt" href="#E43:61"><i><font color="Green" title="E74">A29</font></i></a>, <a class="ref" href="algspec1.html#T4" target="_self" title="ALGSPEC1:th.4">Th4</a>, <a class="ref" href="funct_4.html#T73" title="FUNCT_4:th.73">FUNCT_4:73</a></i>
<br/>.= 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c11">F2</font> <a href="lang1.html#K16" title="LANG1:func.16">*</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c7">g2</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="#E3:61"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="algspec1.html#T38" target="_self" title="ALGSPEC1:th.38">Th38</a>, <a class="ref" href="algspec1.html#T54" target="_self" title="ALGSPEC1:th.54">Th54</a></i>
<br/>.= 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)
<b>by </b><i><a class="txt" href="#E2:61"><i><font color="Green" title="E47">A2</font></i></a>, <a class="txt" href="#E3:61"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="algspec1.html#T38" target="_self" title="ALGSPEC1:th.38">Th38</a>, <a class="ref" href="algspec1.html#T54" target="_self" title="ALGSPEC1:th.54">Th54</a></i>
;<br/>
<b>hence </b><a NAME="E45:61"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S2</font> <a href="algspec1.html#K2" title="ALGSPEC1:func.2">with-replacement</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E7:61"><i><font color="Green" title="E51">A6</font></i></a>, <a class="txt" href="#E8:61"><i><font color="Green" title="E52">A7</font></i></a>, <a class="txt" href="#E11:61"><i><font color="Green" title="E54">A9</font></i></a>, <a class="txt" href="#E12:61"><i><font color="Green" title="E55">A10</font></i></a>, <a class="txt" href="#E25:61"><i><font color="Green" title="E65">A20</font></i></a>, <a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
