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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">ff</font> = 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>;<br/>
<b>set </b><font color="Maroon">gg</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>;<br/>
<b>set </b><font color="Maroon">S'</font> = <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>;<br/>
<b>thus </b><a NAME="E1:45"/>
( <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> implies 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> <font color="Maroon">f</font>,<font color="Maroon">g</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E2:45"/>
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> <font color="Maroon">f</font>,<font color="Maroon">g</font>
 ;<br/>

<a NAME="E3:45"/><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="algspec1.html#R1" target="_self">form_a_replacement_in</a> <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:45"/>
<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/>;<br/>


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