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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">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>





<b>set </b><font color="Maroon">X</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>;<br/>
<b>set </b><font color="Maroon">Y</font> = the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>;<br/>
<b>set </b><font color="Maroon">S2</font> = <font color="Maroon">S</font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font>;<br/>
<b>assume </b><a NAME="E1:48"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="algspec1.html#R1" target="_self">form_a_replacement_in</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E2:48"/><b>then </b><i><font color="Green">E26</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">g</font> <a href="algspec1.html#R1" target="_self">form_a_replacement_in</a> <font color="Maroon">S</font>
 
<b>by </b><i><a class="txt" href="algspec1.html#E3:48"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E3:48"/><i><font color="Green">E27</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font></span>)</span> <a href="pboole.html#R6">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:48"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="algspec1.html#R1" target="_self">form_a_replacement_in</a> <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="txt" href="algspec1.html#E3:48"><i><font color="Green">E27</font></i></a></i>;<br/>
<a NAME="E5:48"/><b>then </b>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">g</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S</font>,<font color="Maroon">S</font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font></span>)</span> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <span class="p2">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">g</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="algspec1.html#T5" target="_self">Th5</a>, </i>;<br/>
<b>hence </b><a NAME="E6:48"/>
<font color="Maroon">S</font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <a href="algspec1.html#K1" target="_self">-indexing</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> <a href="algspec1.html#K2" target="_self">with-replacement</a> <font color="Maroon">f</font>,<font color="Maroon">g</font>
 <b>by </b><i>, </i>;<br/>


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