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<b>let </b><font color="Maroon">U1</font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">U2</font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/>



<b>assume </b><a NAME="E1:19"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">U1</font>,<font color="Maroon">U2</font> <a href="unialg_2.html#R1">are_similar</a> 
 ;<br/>

<a NAME="E2:19"/><b>then </b><i><font color="Green">E46</font></i>: 
 <a href="msualg_1.html#K6">signature</a> <font color="Maroon">U1</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K6">signature</a> <font color="Maroon">U2</font>
 
<b>by </b><i><a class="ref" href="unialg_2.html#D2">UNIALG_2:def 2</a></i>;<br/>
<b>let </b><font color="Maroon">o</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span>;<br/>

<b>set </b><font color="Maroon">A</font> = <span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U2</font></span>)</span> <a href="msuhom_1.html#K2" target="_self">Over</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span>;<br/>
<a NAME="E3:19"/><i><font color="Green">E50</font></i>: 
 <a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:19"/><i><font color="Green">E51</font></i>: 
 <a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U2</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# <span class="p1">(<span class="default"><a href="msualg_1.html#K8">MSSorts</a> <font color="Maroon">U2</font></span>)</span>,<span class="p1">(<span class="default"><a href="msualg_1.html#K9">MSCharact</a> <font color="Maroon">U2</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="msualg_1.html#D16">MSUALG_1:def 16</a></i>;<br/>
<i><font color="Green">E52</font></i>:  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U2</font></span>)</span> <a href="msuhom_1.html#K2" target="_self">Over</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span></span>)</span> = 
the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U2</font></span>)</span> <a href="msuhom_1.html#K2" target="_self">Over</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D11">MSUALG_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_1.html#K9">MSCharact</a> <font color="Maroon">U2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
<b>by </b><i>, , </i>
<br/>.= 
the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">o</font>
<b>by </b><i><a class="ref" href="msualg_1.html#D15">MSUALG_1:def 15</a></i>
;<br/>
<a NAME="E6:19"/><i><font color="Green">E53</font></i>: 
the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="msualg_1.html#D5">MSUALG_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><a href="pboole.html#K8">*--&gt;</a> 0</span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">U1</font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">U1</font></span>)</span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="msualg_1.html#T7">MSUALG_1:7</a></i>;<br/>
<a NAME="E8:19"/><i><font color="Green">E54</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">U1</font></span>)</span> &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span> <a href="funct_2.html#R1">=</a> <font color="Maroon">f</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4">dom</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">U1</font></span>)</span></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="msualg_1.html#D13">MSUALG_1:def 13</a></i>;<br/>
<a NAME="E9:19"/><i><font color="Green">E55</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K6">signature</a> <font color="Maroon">U1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:19"/><b>then </b>
 <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U2</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E11:19"/>
 <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U2</font></span>)</span> <a href="msuhom_1.html#K2" target="_self">Over</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span></span>)</span> is   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U2</font>
 <b>by </b><i>, , , , <a class="ref" href="unialg_2.html#T6">UNIALG_2:6</a></i>;<br/>


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