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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<a NAME="E1:105"/><i><font color="Green">E59</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <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>1</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:105_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="circcomb.html#V6" target="_self">Boolean</a>
 ;<br/><a NAME="E2:105_1"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="pre_circ.html#K2">--&gt;</a> <a href="circcomb.html#K10" target="_self">BOOLEAN</a> 
 <b>by </b><i><a class="ref" href="circcomb.html#T65" target="_self">Th65</a></i>;<br/><b>hence </b><a NAME="E3:105_1"/>
 <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="circcomb.html#K10" target="_self">BOOLEAN</a> </span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:105"/><i><font color="Green">E60</font></i>: 
 <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="circcomb.html#K10" target="_self">BOOLEAN</a> </span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="msafree2.html#NM1">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D15" target="_self">CIRCCOMB:def 15</a><br/>

<a NAME="E4:105"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="circcomb.html#E1:105"><i><font color="Green">E59</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:105"/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="circcomb.html#K10" target="_self">BOOLEAN</a> 
 <b>by </b><i><a class="txt" href="circcomb.html#E3:105"><i><font color="Green">E60</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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