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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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/>

<span class="kw">assume </span><a NAME="E1:61"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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/>

<a NAME="E2:61"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
 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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="circcomb.html#D1" title="CIRCCOMB:def.1">CIRCCOMB:def 1</a></span>;<br/>
<a NAME="E3:61"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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="E4:61"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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="E5:61"/><span class="lab"><font color="Green" title="E50">A5</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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>
 
;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">S</font> = <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>;<br/>
<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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/>

<span class="kw">assume </span><a NAME="E6:61"/><span class="lab"><font color="Green" title="E51">A6</font></span>: 
<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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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/>

<span class="kw">deffunc </span><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>) <span class="kw">-&gt; </span>  <a href="pboole.html#NM1" title="PBOOLE:NM.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/>
<span class="kw">deffunc </span><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>) <span class="kw">-&gt; </span>  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/>
<a NAME="E7:61"/><span class="lab"><font color="Green" title="E52">A7</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <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>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E8:61"/><span class="lab"><font color="Green" title="E53">A8</font></span>: 
<font color="Maroon">H<sub>1</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>1</sub></font>(<font color="Maroon" title="c2">S2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T19" target="_self" title="ALGSPEC1:th.19">Th20</a></span>;<br/>
<a NAME="E9:61"/><span class="lab"><font color="Green" title="E54">A9</font></span>: 
<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="algspec1.html#T47" target="_self" title="ALGSPEC1:th.47">Th49</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">F1</font> = <font color="Maroon">H<sub>1</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>2</sub></font>(<font color="Maroon" title="c1">S1</font>) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="algspec1.html#T36" target="_self" title="ALGSPEC1:th.36">Th37</a>, <a class="ref" href="algspec1.html#T52" target="_self" title="ALGSPEC1:th.52">Th54</a></span>;<br/>
<a NAME="E11:61"/><span class="lab"><font color="Green" title="E55">A10</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">deffunc </span><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>) <span class="kw">-&gt; </span>  <a href="pboole.html#NM1" title="PBOOLE:NM.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="E12:61"/><span class="lab"><font color="Green" title="E56">A11</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <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>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E13:61"/><span class="lab"><font color="Green" title="E57">A12</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">g1</font> =  the    <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>);<br/>
<span class="kw">set </span><font color="Maroon" title="c8">g2</font> =  the    <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="E14:61"/><span class="lab"><font color="Green" title="E58">A13</font></span>: 
 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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>;<br/>
<a NAME="E15:61"/><span class="lab"><font color="Green" title="E59">A14</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a>  the    <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>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T23" target="_self" title="ALGSPEC1:th.23">Th24</a></span>;<br/>
<a NAME="E16:61"/><span class="lab"><font color="Green" title="E60">A15</font></span>: 
 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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>;<br/>
<a NAME="E17:61"/><span class="kw">then </span>
<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T20" target="_self" title="ALGSPEC1:th.20">Th21</a></span>;<br/>
<a NAME="E18:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A16</font></span>: 
 <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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T12" title="RELAT_1:th.12">RELAT_1:12</a></span>;<br/>
<a NAME="E19:61"/><span class="lab"><font color="Green" title="E62">A17</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E20:61"/><span class="lab"><font color="Green" title="E63">A18</font></span>: 
<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T48" target="_self" title="ALGSPEC1:th.48">Th50</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">F2</font> = <font color="Maroon">H<sub>1</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>2</sub></font>(<font color="Maroon" title="c2">S2</font>) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="algspec1.html#T36" target="_self" title="ALGSPEC1:th.36">Th37</a>, <a class="ref" href="algspec1.html#T52" target="_self" title="ALGSPEC1:th.52">Th54</a></span>;<br/>
<a NAME="E22:61"/><span class="lab"><font color="Green" title="E64">A19</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E23:61"/><span class="lab"><font color="Green" title="E65">A20</font></span>: 
 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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>;<br/>
<a NAME="E24:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A21</font></span>: 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T18" target="_self" title="ALGSPEC1:th.18">Th19</a></span>;<br/>
<a NAME="E25:61"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:61"><span class="lab"><font color="Green" title="E65">A20</font></span></a>, <a class="ref" href="algspec1.html#T20" target="_self" title="ALGSPEC1:th.20">Th21</a></span>;<br/>
<a NAME="E26:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A22</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>1</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>1</sub></font>(<font color="Maroon" title="c2">S2</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T12" title="RELAT_1:th.12">RELAT_1:12</a></span>;<br/>
<a NAME="E27:61"/><span class="lab"><font color="Green" title="E68">A23</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E28:61"/><span class="lab"><font color="Green" title="E69">A24</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E29:61"/>
<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c2">S2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:61"><span class="lab"><font color="Green" title="E60">A15</font></span></a>, <a class="ref" href="algspec1.html#T18" target="_self" title="ALGSPEC1:th.18">Th19</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c10">gg</font> =  the    <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="funct_4.html#K1" title="FUNCT_4:func.1">+*</a>  the    <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>) 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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>) <span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T19" target="_self" title="ALGSPEC1:th.19">Th20</a>, <a class="ref" href="algspec1.html#T27" target="_self" title="ALGSPEC1:th.27">Th28</a></span>;<br/>
<a NAME="E31:61"/><span class="lab"><font color="Green" title="E70">A25</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a>  the    <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="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Maroon" title="c1">S1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T23" target="_self" title="ALGSPEC1:th.23">Th24</a></span>;<br/>
<span class="lab"><font color="Green" title="E71">A26</font></span>:  the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>) = 
<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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>) <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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#K2" title="CIRCCOMB:func.2">+*</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="c10">gg</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="algspec1.html#T38" target="_self" title="ALGSPEC1:th.38">Th39</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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="c10">gg</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:61"><span class="lab"><font color="Green" title="E58">A13</font></span></a>, <a class="txt" href="#E24:61"><span class="lab"><font color="Green" title="E66">A21</font></span></a>, <a class="txt" href="#E5:61"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="txt" href="#E12:61"><span class="lab"><font color="Green" title="E56">A11</font></span></a>, <a class="txt" href="#E7:61"><span class="lab"><font color="Green" title="E52">A7</font></span></a>, <a class="ref" href="algspec1.html#T19" target="_self" title="ALGSPEC1:th.19">Th20</a>, <a class="ref" href="funct_4.html#T69" title="FUNCT_4:th.69">FUNCT_4:69</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>) <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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>  the    <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>)</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>1</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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>  the    <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>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:61"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="txt" href="#E31:61"><span class="lab"><font color="Green" title="E70">A25</font></span></a>, <a class="txt" href="#E15:61"><span class="lab"><font color="Green" title="E59">A14</font></span></a>, <a class="txt" href="#E13:61"><span class="lab"><font color="Green" title="E57">A12</font></span></a>, <a class="txt" href="#E19:61"><span class="lab"><font color="Green" title="E62">A17</font></span></a>, <a class="txt" href="#E11:61"><span class="lab"><font color="Green" title="E55">A10</font></span></a>, <a class="txt" href="#E22:61"><span class="lab"><font color="Green" title="E64">A19</font></span></a>, <a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="ref" href="algspec1.html#T4" target="_self" title="ALGSPEC1:th.4">Th4</a>, <a class="ref" href="funct_4.html#T69" title="FUNCT_4:th.69">FUNCT_4:69</a></span>
<br/>.= 
 the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>2</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>1</sub></font>(<font color="Maroon" title="c2">S2</font>) <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</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>  the    <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>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E54">A9</font></span></a>, <a class="ref" href="algspec1.html#T38" target="_self" title="ALGSPEC1:th.38">Th39</a>, <a class="ref" href="algspec1.html#T52" target="_self" title="ALGSPEC1:th.52">Th54</a></span>
<br/>.= 
 the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon">H<sub>2</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>2</sub></font>(<font color="Maroon" title="c2">S2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E20:61"><span class="lab"><font color="Green" title="E63">A18</font></span></a>, <a class="ref" href="algspec1.html#T38" target="_self" title="ALGSPEC1:th.38">Th39</a>, <a class="ref" href="algspec1.html#T52" target="_self" title="ALGSPEC1:th.52">Th54</a></span>
;<br/>
<a NAME="E33:61"/><span class="lab"><font color="Green" title="E72">A27</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="algspec1.html#D4" target="_self" title="ALGSPEC1:def.4">Def4</a></span>;<br/>
<a NAME="E34:61"/><span class="lab"><font color="Green" title="E73">A28</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">FS</font> = <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>) <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="algspec1.html#T36" target="_self" title="ALGSPEC1:th.36">Th37</a></span>;<br/>
<a NAME="E36:61"/><span class="lab"><font color="Green" title="E74">A29</font></span>: 
<span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">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#K2" title="CIRCCOMB:func.2">+*</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#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">FS</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<a NAME="E37:61"/><span class="lab"><font color="Green" title="E75">A30</font></span>: 
 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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>;<br/>
<a NAME="E38:61"/><span class="lab"><font color="Green" title="E76">A31</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E54">A9</font></span></a>, <a class="ref" href="algspec1.html#T52" target="_self" title="ALGSPEC1:th.52">Th54</a></span>;<br/>
<a NAME="E39:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A32</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">S1</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#D4" target="_self" title="ALGSPEC1:def.4">Def4</a></span>;<br/>
<a NAME="E40:61"/><span class="lab"><font color="Green" title="E78">A33</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <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>  <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E38:61"><span class="lab"><font color="Green" title="E76">A31</font></span></a>, <a class="ref" href="algspec1.html#D4" target="_self" title="ALGSPEC1:def.4">Def4</a></span>;<br/>
<a NAME="E41:61"/><span class="lab"><font color="Green" title="E79">A34</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="algspec1.html#D4" target="_self" title="ALGSPEC1:def.4">Def4</a></span>;<br/>
<a NAME="E42:61"/><span class="lab"><font color="Green" title="E80">A35</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E43:61"/>
 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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="circcomb.html#D1" title="CIRCCOMB:def.1">CIRCCOMB:def 1</a></span>;<br/>
<a NAME="E44:61"/><span class="kw">then </span>
 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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:61"><span class="lab"><font color="Green" title="E75">A30</font></span></a>, <a class="ref" href="funct_4.html#T30" title="FUNCT_4:th.30">FUNCT_4:30</a></span>;<br/>
<a NAME="E45:61"/><span class="kw">then </span>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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#K2" title="CIRCCOMB:func.2">+*</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#K2" title="RELSET_1:func.2">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#K2" title="RELSET_1:func.2">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T12" title="RELAT_1:th.12">RELAT_1:12</a></span>;<br/>
<a NAME="E46:61"/><span class="kw">then </span>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T13" title="XBOOLE_1:th.13">XBOOLE_1:13</a></span>;<br/>
<a NAME="E47:61"/><span class="kw">then </span>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:61"><span class="lab"><font color="Green" title="E80">A35</font></span></a>, <a class="txt" href="#E28:61"><span class="lab"><font color="Green" title="E69">A24</font></span></a>, <a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>;<br/>
<a NAME="E48:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A36</font></span>: 
<span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">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#K2" title="CIRCCOMB:func.2">+*</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#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">FS</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:61"><span class="lab"><font color="Green" title="E74">A29</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E49:61"/><span class="lab"><font color="Green" title="E82">A37</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E20:61"><span class="lab"><font color="Green" title="E63">A18</font></span></a>, <a class="ref" href="algspec1.html#T52" target="_self" title="ALGSPEC1:th.52">Th54</a></span>;<br/>
<a NAME="E50:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A38</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">S2</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#D4" target="_self" title="ALGSPEC1:def.4">Def4</a></span>;<br/>
<a NAME="E51:61"/><span class="lab"><font color="Green" title="E84">A39</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <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>  <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E49:61"><span class="lab"><font color="Green" title="E82">A37</font></span></a>, <a class="ref" href="algspec1.html#D4" target="_self" title="ALGSPEC1:def.4">Def4</a></span>;<br/>
<a NAME="E52:61"/><span class="lab"><font color="Green" title="E85">A40</font></span>: 
<font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a>  <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> <font color="Maroon" title="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T6" target="_self" title="ALGSPEC1:th.6">Th6</a>, <a class="ref" href="algspec1.html#T19" target="_self" title="ALGSPEC1:th.19">Th20</a></span>;<br/>
<a NAME="E53:61"/><span class="lab"><font color="Green" title="E86">A41</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T29" title="FUNCT_4:th.29">FUNCT_4:29</a></span>;<br/>
<a NAME="E54:61"/>
<font color="Maroon" title="c9">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:61"><span class="lab"><font color="Green" title="E65">A20</font></span></a>, <a class="ref" href="algspec1.html#T17" target="_self" title="ALGSPEC1:th.17">Th18</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E55:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A42</font></span>: 
<font color="Maroon" title="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a>  <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c11">FS</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T5" target="_self" title="ALGSPEC1:th.5">Th5</a>, <a class="ref" href="relat_1.html#T59" title="RELAT_1:th.59">RELAT_1:59</a></span>;<br/>
<a NAME="E56:61"/>
<font color="Maroon" title="c6">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:61"><span class="lab"><font color="Green" title="E65">A20</font></span></a>, <a class="ref" href="algspec1.html#T17" target="_self" title="ALGSPEC1:th.17">Th18</a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/>
<a NAME="E57:61"/><span class="kw">then </span>
<font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a>  <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <font color="Maroon" title="c11">FS</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T5" target="_self" title="ALGSPEC1:th.5">Th5</a>, <a class="ref" href="relat_1.html#T59" title="RELAT_1:th.59">RELAT_1:59</a></span>;<br/>
<a NAME="E58:61"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">FS</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:61"><span class="lab"><font color="Green" title="E87">A42</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/>
<a NAME="E59:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A43</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">FS</font> <a href="lang1.html#K12" title="LANG1:func.12">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:61"><span class="lab"><font color="Green" title="E86">A41</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<a NAME="E60:61"/><span class="lab"><font color="Green" title="E89">A44</font></span>: 
 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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="circcomb.html#D1" title="CIRCCOMB:def.1">CIRCCOMB:def 1</a></span>;<br/>
<a NAME="E61:61"/><span class="lab"><font color="Green" title="E90">A45</font></span>: 
 <a href="relset_1.html#K2" title="RELSET_1:func.2">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> 
 
;<br/>
 the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font>) = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">FS</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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#K2" title="CIRCCOMB:func.2">+*</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="c10">gg</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="ref" href="algspec1.html#T37" target="_self" title="ALGSPEC1:th.37">Th38</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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#K2" title="CIRCCOMB:func.2">+*</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="c10">gg</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:61"><span class="lab"><font color="Green" title="E88">A43</font></span></a>, <a class="txt" href="#E48:61"><span class="lab"><font color="Green" title="E81">A36</font></span></a>, <a class="ref" href="algspec1.html#T2" target="_self" title="ALGSPEC1:th.2">Th2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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="c10">gg</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:61"><span class="lab"><font color="Green" title="E75">A30</font></span></a>, <a class="txt" href="#E8:61"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="txt" href="#E61:61"><span class="lab"><font color="Green" title="E90">A45</font></span></a>, <a class="txt" href="#E3:61"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="txt" href="#E42:61"><span class="lab"><font color="Green" title="E80">A35</font></span></a>, <a class="txt" href="#E28:61"><span class="lab"><font color="Green" title="E69">A24</font></span></a>, <a class="ref" href="algspec1.html#T6" target="_self" title="ALGSPEC1:th.6">Th6</a>, <a class="ref" href="funct_4.html#T69" title="FUNCT_4:th.69">FUNCT_4:69</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">F1</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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>  the    <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>)</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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>  the    <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>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:61"><span class="lab"><font color="Green" title="E70">A25</font></span></a>, <a class="txt" href="#E15:61"><span class="lab"><font color="Green" title="E59">A14</font></span></a>, <a class="txt" href="#E13:61"><span class="lab"><font color="Green" title="E57">A12</font></span></a>, <a class="txt" href="#E19:61"><span class="lab"><font color="Green" title="E62">A17</font></span></a>, <a class="txt" href="#E52:61"><span class="lab"><font color="Green" title="E85">A40</font></span></a>, <a class="txt" href="#E60:61"><span class="lab"><font color="Green" title="E89">A44</font></span></a>, <a class="txt" href="#E34:61"><span class="lab"><font color="Green" title="E73">A28</font></span></a>, <a class="txt" href="#E27:61"><span class="lab"><font color="Green" title="E68">A23</font></span></a>, <a class="ref" href="algspec1.html#T4" target="_self" title="ALGSPEC1:th.4">Th4</a>, <a class="ref" href="funct_4.html#T69" title="FUNCT_4:th.69">FUNCT_4:69</a></span>
<br/>.= 
 the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>2</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="c9">F2</font> <a href="lang1.html#K12" title="LANG1:func.12">*</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>  the    <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>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E54">A9</font></span></a>, <a class="ref" href="algspec1.html#T37" target="_self" title="ALGSPEC1:th.37">Th38</a>, <a class="ref" href="algspec1.html#T52" target="_self" title="ALGSPEC1:th.52">Th54</a></span>
<br/>.= 
 the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon">H<sub>2</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>2</sub></font>(<font color="Maroon" title="c2">S2</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E20:61"><span class="lab"><font color="Green" title="E63">A18</font></span></a>, <a class="ref" href="algspec1.html#T37" target="_self" title="ALGSPEC1:th.37">Th38</a>, <a class="ref" href="algspec1.html#T52" target="_self" title="ALGSPEC1:th.52">Th54</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E63:61"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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#K2" title="CIRCCOMB:func.2">+*</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E26:61"><span class="lab"><font color="Green" title="E67">A22</font></span></a>, <a class="txt" href="#E33:61"><span class="lab"><font color="Green" title="E72">A27</font></span></a>, <a class="txt" href="#E39:61"><span class="lab"><font color="Green" title="E77">A32</font></span></a>, <a class="txt" href="#E50:61"><span class="lab"><font color="Green" title="E83">A38</font></span></a>, <a class="txt" href="#E18:61"><span class="lab"><font color="Green" title="E61">A16</font></span></a>, <a class="txt" href="#E41:61"><span class="lab"><font color="Green" title="E79">A34</font></span></a>, <a class="txt" href="#E40:61"><span class="lab"><font color="Green" title="E78">A33</font></span></a>, <a class="txt" href="#E51:61"><span class="lab"><font color="Green" title="E84">A39</font></span></a>, <a class="txt" href="#E32:61"><span class="lab"><font color="Green" title="E71">A26</font></span></a>, <a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
