<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><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>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="relat_1.html#V2">V3</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<a NAME="E1:10"/><i><font color="Green">E7</font></i>: 
 <a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="msafree.html#K10">FreeOper</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msafree.html#D16">MSAFREE:def 16</a></i>;<br/>
<font color="Maroon">c<sub>2</sub></font> <a href="msaterm.html#K1">-Terms</a> <font color="Maroon">c<sub>3</sub></font> = 
 <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5">DTConMSA</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="msaterm.html#D1">MSATERM:def 1</a></i>
<br/>.= 
 <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="msafree.html#T12">MSAFREE:12</a></i>
<br/>.= 
 <a href="card_3.html#K3">Union</a> <span class="p1">(<span class="default"><a href="msafree.html#K8">FreeSort</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_3.html#D4">CARD_3:def 4</a></i>
;<br/>
<b>hence </b><a NAME="E3:10"/>
( <font color="Maroon">c<sub>1</sub></font> is   <a href="msafree3.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="msafree.html#K11">FreeMSA</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> iff <font color="Maroon">c<sub>1</sub></font> is   <a href="msaterm.html#NM1">Term</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="msafree3.html#E1:10"><i><font color="Green">E7</font></i></a></i>;<br/>


</div>
