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

<b>thus </b><a NAME="E1:10"/>
<font color="Maroon">U1</font>,<font color="Maroon">U1</font> <a href="unialg_2.html#R1">are_similar</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="alg_1.html#D1" target="_self">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="E2:10"/>
<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>, <font color="Maroon">o2</font> be   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">U1</font>;<br/>

<b>assume </b><a NAME="E3:10"/><i><font color="Green">E33</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> &amp; <font color="Maroon">o2</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> )
 ;<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="E4:10"/>
<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/>

<a NAME="E5:10"/><b>then </b>
( <font color="Maroon">o1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">o1</font> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">o1</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">u</font> = <font color="Maroon">o1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">U1</font> ;<br/>
<b>set </b><font color="Maroon">f</font> =  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font>;<br/>
<a NAME="E7:10"/>
( <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> )
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T35">FUNCT_1:35</a></i>;<br/>
<b>hence </b><a NAME="E8:10"/>
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font></span>)</span> <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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font></span>)</span> <a href="finseqop.html#K5">*</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i/>;<br/>


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