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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">m1</font> be   <a href="monoid_1.html#NM2">Multiset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">m2</font> be   <a href="monoid_1.html#NM2">Multiset</a> of <font color="Maroon">A</font>;<br/>





<b>assume </b><a NAME="E1:57"/>
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font> holds  <font color="Maroon">m1</font> <a href="monoid_1.html#K15" target="_self">.</a> <font color="Olive">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</font> <a href="monoid_1.html#K15" target="_self">.</a> <font color="Olive">a</font>
 ;<br/>

<a NAME="E2:57"/><b>then </b>
( ( for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Maroon">m1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> ) &amp;  <a href="monoid_1.html#K13" target="_self">MultiSet_over</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="monoid_1.html#K12" target="_self">.:</a> <a href="monoid_0.html#K6">&lt;NAT,+,0&gt;</a> ,<font color="Maroon">A</font> )
 
;<br/>
<b>hence </b><a NAME="E3:57"/>
<font color="Maroon">m1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m2</font>
 <b>by </b><i/>;<br/>


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