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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="msualg_1.html#V2">void</a> <a href="catalg_1.html#NM1">Signature</a>;<br/>

<b>assume </b><a NAME="E1:63"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#R1">tolerates</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E2:63"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="algspec1.html#R1" target="_self">form_a_replacement_in</a> <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>( non <a href="msualg_1.html#V2">void</a> <a href="catalg_1.html#NM1">Signature</a>) <b>-&gt; </b> 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="msualg_1.html#L1">ManySortedSign</a>  = <font color="Maroon">a<sub>1</sub></font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>( non <a href="msualg_1.html#V2">void</a> <a href="catalg_1.html#NM1">Signature</a>) <b>-&gt; </b>   <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">a<sub>1</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">a<sub>1</sub></font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>( non <a href="msualg_1.html#V2">void</a> <a href="catalg_1.html#NM1">Signature</a>) <b>-&gt; </b>   <a href="pboole.html#M1">ManySortedSet</a> of the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">a<sub>1</sub></font> = the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">a<sub>1</sub></font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E3:63"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font> is    <a href="algspec1.html#M2" target="_self">Extension</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font> is    <a href="algspec1.html#M2" target="_self">Extension</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="algspec1.html#E1:63"><i><font color="Green">E48</font></i></a>, <a class="ref" href="algspec1.html#T49" target="_self">Th49</a>, <a class="ref" href="algspec1.html#T50" target="_self">Th50</a></i>;<br/>
<a NAME="E4:63"/><b>then </b><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="algspec1.html#R1" target="_self">form_a_replacement_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="algspec1.html#R1" target="_self">form_a_replacement_in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="algspec1.html#E2:63"><i><font color="Green">E49</font></i></a>, <a class="ref" href="algspec1.html#T54" target="_self">Th54</a></i>;<br/>
<a NAME="E5:63"/><i><font color="Green">E51</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="circcomb.html#K3">+*</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>)</span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E6:63"/><b>then </b>
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="xboole_0.html#K2">\/</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>)
 
<b>by </b><i><a class="ref" href="algspec1.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E7:63"/><b>then </b><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>)</span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E8:63"/><i><font color="Green">E53</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="txt" href="algspec1.html#E2:63"><i><font color="Green">E49</font></i></a>, <a class="txt" href="algspec1.html#E4:63"><i><font color="Green">E50</font></i></a>, <a class="ref" href="algspec1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E9:63"/><i><font color="Green">E54</font></i>: 
( the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="circcomb.html#K3">+*</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>)</span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E10:63"/><b>then </b>
<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="xboole_0.html#K2">\/</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>)
 
<b>by </b><i><a class="ref" href="algspec1.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E11:63"/><b>then </b><i><font color="Green">E55</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>)</span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>)</span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E12:63"/><i><font color="Green">E56</font></i>: 
( the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="txt" href="algspec1.html#E2:63"><i><font color="Green">E49</font></i></a>, <a class="txt" href="algspec1.html#E4:63"><i><font color="Green">E50</font></i></a>, <a class="ref" href="algspec1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E13:63"/><i><font color="Green">E57</font></i>: 
( the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="circcomb.html#K3">+*</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>)</span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E14:63"/><i><font color="Green">E58</font></i>: 
( the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="circcomb.html#K3">+*</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>)</span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="algspec1.html#M1" target="_self">rng-retract</a> of <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>), <font color="Maroon">c<sub>7</sub></font> being    <a href="algspec1.html#M1" target="_self">rng-retract</a> of <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>);<br/>
<a NAME="E16:63"/>
( <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) &amp; <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="circcomb.html#K1">+*</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="txt" href="algspec1.html#E9:63"><i><font color="Green">E54</font></i></a>, <a class="ref" href="algspec1.html#T19" target="_self">Th19</a>, <a class="ref" href="algspec1.html#T20" target="_self">Th20</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>7</sub></font> as    <a href="algspec1.html#M1" target="_self">rng-retract</a> of <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <b>by </b><i><a class="ref" href="algspec1.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E18:63"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="circcomb.html#K1">+*</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) &amp; <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="txt" href="algspec1.html#E5:63"><i><font color="Green">E51</font></i></a>, <a class="ref" href="algspec1.html#T19" target="_self">Th19</a>, <a class="ref" href="algspec1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E19:63"/><i><font color="Green">E60</font></i>: 
(  <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<a NAME="E20:63"/><i><font color="Green">E61</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E21:63"/><i><font color="Green">E62</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>7</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) )
 
<b>by </b><i><a class="ref" href="algspec1.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E22:63"/><i><font color="Green">E63</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E23:63"/><i><font color="Green">E64</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E24:63"/>
the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E1:63"><i><font color="Green">E48</font></i></a>, <a class="ref" href="circcomb.html#D1">CIRCCOMB:def 1</a></i>;<br/>
<a NAME="E25:63"/><b>then </b><i><font color="Green">E65</font></i>: 
<font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font> <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E18:63"><i><font color="Green">E59</font></i></a>, <a class="ref" href="algspec1.html#T4" target="_self">Th4</a></i>;<br/>
<i><font color="Green">E66</font></i>: the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) = 
<span class="p1">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="algspec1.html#E2:63"><i><font color="Green">E49</font></i></a>, <a class="ref" href="algspec1.html#T39" target="_self">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">c<sub>1</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="circcomb.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="algspec1.html#E14:63"><i><font color="Green">E58</font></i></a>, <a class="txt" href="algspec1.html#E18:63"><i><font color="Green">E59</font></i></a>, <a class="txt" href="algspec1.html#E19:63"><i><font color="Green">E60</font></i></a>, <a class="txt" href="algspec1.html#E20:63"><i><font color="Green">E61</font></i></a>, <a class="ref" href="funct_4.html#T73">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">c<sub>1</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="algspec1.html#E21:63"><i><font color="Green">E62</font></i></a>, <a class="txt" href="algspec1.html#E22:63"><i><font color="Green">E63</font></i></a>, <a class="txt" href="algspec1.html#E23:63"><i><font color="Green">E64</font></i></a>, <a class="txt" href="algspec1.html#E25:63"><i><font color="Green">E65</font></i></a>, <a class="ref" href="funct_4.html#T73">FUNCT_4:73</a></i>
<br/>.= 
the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="algspec1.html#E4:63"><i><font color="Green">E50</font></i></a>, <a class="ref" href="algspec1.html#T39" target="_self">Th39</a></i>
<br/>.= 
the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>)
<b>by </b><i><a class="txt" href="algspec1.html#E4:63"><i><font color="Green">E50</font></i></a>, <a class="ref" href="algspec1.html#T39" target="_self">Th39</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) <b>by </b><i><a class="txt" href="algspec1.html#E2:63"><i><font color="Green">E49</font></i></a>, <a class="ref" href="algspec1.html#T37" target="_self">Th37</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>1</sub></font>) as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <b>by </b><i><a class="txt" href="algspec1.html#E4:63"><i><font color="Green">E50</font></i></a>, <a class="ref" href="algspec1.html#T37" target="_self">Th37</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>2</sub></font>) as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <b>by </b><i><a class="txt" href="algspec1.html#E4:63"><i><font color="Green">E50</font></i></a>, <a class="ref" href="algspec1.html#T37" target="_self">Th37</a></i>;<br/>
<a NAME="E30:63"/>
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E1:63"><i><font color="Green">E48</font></i></a>, <a class="ref" href="circcomb.html#D1">CIRCCOMB:def 1</a></i>;<br/>
<a NAME="E31:63"/><b>then </b>
the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E13:63"><i><font color="Green">E57</font></i></a>, <a class="ref" href="funct_4.html#T31">FUNCT_4:31</a></i>;<br/>
<a NAME="E32:63"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T26">RELAT_1:26</a></i>;<br/>
<a NAME="E33:63"/><i><font color="Green">E68</font></i>: 
(  <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a>  &amp;  <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K3">*</a>  )
 
;<br/>
<a NAME="E34:63"/><i><font color="Green">E69</font></i>: 
 <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K3">*</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="algspec1.html#E32:63"><i><font color="Green">E67</font></i></a>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E35:63"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="algspec1.html#E5:63"><i><font color="Green">E51</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E36:63"/><b>then </b>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="algspec1.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E37:63"/><b>then </b>
( <font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T88">RELAT_1:88</a></i>;<br/>
<a NAME="E38:63"/><b>then </b>
( <font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> <a href="lang1.html#K16">*</a>  &amp; <font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> <a href="lang1.html#K16">*</a>  )
 
<b>by </b><i><a class="ref" href="algspec1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E39:63"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> <a href="lang1.html#K16">*</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T30">FUNCT_4:30</a>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E40:63"/><b>then </b><i><font color="Green">E70</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> <a href="lang1.html#K16">*</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E41:63"/><i><font color="Green">E71</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a>  &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E42:63"/><b>then </b>
(  <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="lang1.html#K16">*</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="algspec1.html#E34:63"><i><font color="Green">E69</font></i></a>, <a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E43:63"/><b>then </b><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="lang1.html#K16">*</a> </span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E44:63"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a>  <a href="partfun1.html#R1">tolerates</a> <font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> 
 
<b>by </b><i><a class="txt" href="algspec1.html#E18:63"><i><font color="Green">E59</font></i></a>, <a class="ref" href="algspec1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E45:63"/>
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E1:63"><i><font color="Green">E48</font></i></a>, <a class="ref" href="circcomb.html#D1">CIRCCOMB:def 1</a></i>;<br/>
<a NAME="E46:63"/><b>then </b><i><font color="Green">E74</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font> <a href="partfun1.html#R1">tolerates</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E44:63"><i><font color="Green">E73</font></i></a>, <a class="ref" href="algspec1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E47:63"/><i><font color="Green">E75</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="algspec1.html#E2:63"><i><font color="Green">E49</font></i></a>, <a class="ref" href="algspec1.html#T38" target="_self">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">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="algspec1.html#E40:63"><i><font color="Green">E70</font></i></a>, <a class="txt" href="algspec1.html#E43:63"><i><font color="Green">E72</font></i></a>, <a class="ref" href="algspec1.html#T2" target="_self">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">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="algspec1.html#E13:63"><i><font color="Green">E57</font></i></a>, <a class="txt" href="algspec1.html#E33:63"><i><font color="Green">E68</font></i></a>, <a class="txt" href="algspec1.html#E41:63"><i><font color="Green">E71</font></i></a>, <a class="txt" href="algspec1.html#E44:63"><i><font color="Green">E73</font></i></a>, <a class="ref" href="funct_4.html#T73">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">c<sub>10</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="algspec1.html#E21:63"><i><font color="Green">E62</font></i></a>, <a class="txt" href="algspec1.html#E22:63"><i><font color="Green">E63</font></i></a>, <a class="txt" href="algspec1.html#E46:63"><i><font color="Green">E74</font></i></a>, <a class="txt" href="algspec1.html#E47:63"><i><font color="Green">E75</font></i></a>, <a class="ref" href="funct_4.html#T73">FUNCT_4:73</a></i>
<br/>.= 
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="lang1.html#K16">*</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="algspec1.html#E4:63"><i><font color="Green">E50</font></i></a>, <a class="ref" href="algspec1.html#T38" target="_self">Th38</a></i>
<br/>.= 
the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>2</sub></font>)
<b>by </b><i><a class="txt" href="algspec1.html#E4:63"><i><font color="Green">E50</font></i></a>, <a class="ref" href="algspec1.html#T38" target="_self">Th38</a></i>
;<br/>
<b>hence </b><a NAME="E49:63"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="algspec1.html#K2" target="_self">with-replacement</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="circcomb.html#K3">+*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="algspec1.html#E7:63"><i><font color="Green">E52</font></i></a>, <a class="txt" href="algspec1.html#E8:63"><i><font color="Green">E53</font></i></a>, <a class="txt" href="algspec1.html#E11:63"><i><font color="Green">E55</font></i></a>, <a class="txt" href="algspec1.html#E12:63"><i><font color="Green">E56</font></i></a>, <a class="txt" href="algspec1.html#E26:63"><i><font color="Green">E66</font></i></a>, <a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>;<br/>


</div>
