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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>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">U1</font>,<font color="Maroon">U2</font>;<br/>





<b>assume </b><a NAME="E1:28"/><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/>

<b>set </b><font color="Maroon">f</font> =  <a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">h</font>;<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="E2:28"/><i><font color="Green">E46</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/>
<b>assume </b><a NAME="E3:28"/><i><font color="Green">E50</font></i>: 
 <a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">h</font> <a href="msualg_3.html#R1">is_homomorphism</a>  <a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U1</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/>

<b>thus </b><a NAME="E4:28"/>
<font color="Maroon">U1</font>,<font color="Maroon">U2</font> <a href="unialg_2.html#R1">are_similar</a> 
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="alg_1.html#D1">ALG_1:def 1</a><br/>

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E5:28"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font>
 ;<br/>

<b>let </b><font color="Maroon">O1</font> be   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U1</font>;<br/><b>let </b><font color="Maroon">O2</font> be   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U2</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E6:28"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">O1</font> <a href="hidden.html#R1">=</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">U1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E7:28"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">O2</font> <a href="hidden.html#R1">=</a> 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">n</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">U1</font>;<br/>

<b>assume </b><a NAME="E8:28"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">O1</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">o</font> = <font color="Maroon">n</font> as   <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> <b>by </b><i>, </i>;<br/>
<a NAME="E10:28"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">O1</font> <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U1</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>then reconsider </b><font color="Maroon">y</font> = <font color="Maroon">x</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">o</font>,<span class="p1">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U1</font></span>)</span> <b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E12:28"/><i><font color="Green">E57</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">h</font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<span class="p3">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">O1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font></span>)</span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E13:28"/><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">h</font></span>)</span> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="msualg_1.html#K2">the_result_sort_of</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<span class="p3">(<span class="default"><a href="msualg_1.html#K10">MSAlg</a> <font color="Maroon">U1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msualg_1.html#K5">Den</a> <font color="Maroon">o</font>,<span class="p2">(<span class="default"><span class="p3">(<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="p3">(<span class="default"><a href="msualg_1.html#K7">MSSign</a> <font color="Maroon">U1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msuhom_1.html#K3" target="_self">MSAlg</a> <font color="Maroon">h</font></span>)</span> <a href="msualg_3.html#K6">#</a> <font color="Maroon">y</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="msualg_3.html#D9">MSUALG_3:def 9</a></i>;<br/>
<a NAME="E14:28"/><i><font color="Green">E59</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/>
 <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/>.= 
<font color="Maroon">O2</font>
<b>by </b><i>, <a class="ref" href="msualg_1.html#D15">MSUALG_1:def 15</a></i>
;<br/>
<b>hence </b><a NAME="E16:28"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">O1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">O2</font> <a href="funct_1.html#K1">.</a> <a href="finseqop.html#K5">K143</a>(the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U2</font>,<font color="Maroon">x</font>,<font color="Maroon">h</font>)
 <b>by </b><i>, , , </i>;<br/>


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