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<b>let </b><font color="Maroon">S</font> be  non <a href="msualg_1.html#V2">void</a> <a href="catalg_1.html#NM1">Signature</a>;<br/><b>let </b><font color="Maroon">A</font> be  <a href="msafree1.html#V1">disjoint_valued</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">C1</font> be   <a href="pboole.html#NM3">Component</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font>, <font color="Maroon">C2</font> be   <a href="pboole.html#NM3">Component</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font>;<br/>





<a NAME="E1:73"/>
 <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E2:73"/><b>then </b><i><font color="Green">E25</font></i>: 
 <a href="relat_1.html#K2">rng</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="relat_1.html#T65">RELAT_1:65</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:73"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> &amp; <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:73"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> &amp; <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="algspec1.html#T11" target="_self">Th11</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E7:73"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> is <a href="prob_2.html#V1">disjoint_valued</a> &amp; ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> or <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> ) )
 
<b>by </b><i><a class="ref" href="msafree1.html#D2">MSAFREE1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E8:73"/>
( <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C2</font> or <font color="Maroon">C1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C2</font> )
 <b>by </b><i><a class="ref" href="algspec1.html#T12" target="_self">Th12</a>, <a class="ref" href="algspec1.html#T13" target="_self">Th13</a>, <a class="ref" href="prob_2.html#D3">PROB_2:def 3</a></i>;<br/>


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