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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>



<b>set </b><font color="Maroon">T</font> = <span class="p1">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="circcomb.html#K3">+*</a> <font color="Maroon">S</font>;<br/>
<b>assume </b><a NAME="E1:9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ;<br/>

<a NAME="E2:9"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E3:9"/><b>then </b><i><font color="Green">E25</font></i>: 
( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; <a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>;<br/>
<a NAME="E4:9"/><i><font color="Green">E33</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i>, <a class="ref" href="msualg_1.html#D5">MSUALG_1:def 5</a></i>;<br/>
<a NAME="E5:9"/><b>then </b>
( the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <a href="xboole_0.html#K1">{}</a>  <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> &amp; <a href="xboole_0.html#K1">{}</a>  <a href="funct_4.html#K1">+*</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T21">FUNCT_4:21</a>, <a class="ref" href="relset_1.html#T26">RELSET_1:26</a></i>;<br/>
<a NAME="E6:9"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="circcomb.html#K3">+*</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="circcomb.html#K3">+*</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="circcomb.html#K3">+*</a> <font color="Maroon">S</font></span>)</span> <a href="funct_2.html#R1">=</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="circcomb.html#K3">+*</a> <font color="Maroon">S</font></span>)</span> <a href="funct_2.html#R1">=</a> the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font> )
 
<b>by </b><i>, , <a class="ref" href="circcomb.html#D2">CIRCCOMB:def 2</a></i>;<br/>
<b>hence </b><a NAME="E7:9"/>
<span class="p1">(<span class="default"><a href="facirc_2.html#K1" target="_self">SingleMSS</a> <font color="Maroon">x</font></span>)</span> <a href="circcomb.html#K3">+*</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G1">ManySortedSign</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>,the <a href="msualg_1.html#U2">Arity</a> of <font color="Maroon">S</font>,the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> #)
 ;<br/>


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