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<b>let </b><font color="Maroon">S</font> be   <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">o1</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">o2</font> be   <a href="osalg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="osalg_1.html#NM5">OSAlgebra</a> of <font color="Maroon">S</font>;<br/>







<b>reconsider </b><font color="Maroon">M</font> = the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> as   <a href="osalg_1.html#NM4">OrderSortedSet</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="osalg_1.html#T1" target="_self">Th1</a></i>;<br/>
<b>assume </b><a NAME="E2:72"/>
 <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o1</font> <a href="orders_2.html#R3">&lt;=</a>  <a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o2</font>
 ;<br/>

<a NAME="E3:72"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o1</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">M</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<i><font color="Green">E40</font></i>:  <a href="msualg_1.html#K4">Result</a> <font color="Maroon">o1</font>,<font color="Maroon">A</font> = 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o1</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D10">MSUALG_1:def 10</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">o1</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o1</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D7">MSUALG_1:def 7</a></i>
;<br/>
 <a href="msualg_1.html#K4">Result</a> <font color="Maroon">o2</font>,<font color="Maroon">A</font> = 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o2</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D10">MSUALG_1:def 10</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U3">ResultSort</a> of <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">o2</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="osalg_1.html#K1" target="_self">the_result_sort_of</a> <font color="Maroon">o2</font></span>)</span>
<b>by </b><i><a class="ref" href="msualg_1.html#D7">MSUALG_1:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E6:72"/>
 <a href="msualg_1.html#K4">Result</a> <font color="Maroon">o1</font>,<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="msualg_1.html#K4">Result</a> <font color="Maroon">o2</font>,<font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="osalg_1.html#T2" target="_self">Th2</a>, </i>;<br/>


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