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<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> , <font color="Maroon">S2</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>assume </b><a NAME="E1:34"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="pua2mss1.html#R3">form_morphism_between</a> <font color="Maroon">S1</font>,<font color="Maroon">S2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">g'</font> = <font color="Maroon">g</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S1</font>,the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S2</font> <b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">A</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S2</font>;<br/><b>let </b><font color="Maroon">o1</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S1</font>;<br/><b>let </b><font color="Maroon">o2</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S2</font>;<br/>





<b>assume </b><a NAME="E3:34"/>
<font color="Maroon">o2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o1</font>
 ;<br/>

<b>then </b>the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="msualg_3.html#K1">.</a> <font color="Maroon">o2</font> = 
<span class="p1">(<span class="default">the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> <font color="Maroon">g'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o1</font>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S1</font>,<font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span> <a href="msualg_3.html#K1">.</a> <font color="Maroon">o1</font>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E5:34"/>
 <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o1</font>,<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="instalg1.html#K1" target="_self">|</a> <font color="Maroon">S1</font>,<font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o2</font>,<font color="Maroon">A</font>
 ;<br/>


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