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<b>let </b><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> 
 ;<br/>

<a NAME="E2:12"/><b>then </b>
<span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#G1" title="UNIALG_1:aggr.1">UAStr</a>(# <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="pralg_1.html#K4" title="PRALG_1:func.4">Opers</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="pralg_1.html#D5" target="_self" title="PRALG_1:def.5">Def5</a></i>;<br/>
<a NAME="E3:12"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font>
 
<b>by </b><i><a class="txt" href="pralg_1.html#E1:12"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="pralg_1.html#D4" target="_self" title="PRALG_1:def.4">Def4</a></i>;<br/>
<b>then </b><i><font color="Green" title="E11">A2</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font>
<b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span>
<b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>
;<br/>
<a NAME="E5:12"/><i><font color="Green" title="E12">A3</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <span class="p3"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span>)</span></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:12_2"/><i><font color="Green" title="E13">A4</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:12_2"/><b>then </b><i><font color="Green" title="E14">A5</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font></span>)</span>
 <b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/><a NAME="E3:12_2"/><b>then </b>
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c4">o1</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c1">U1</font> <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E5:12_2"/><i><font color="Green" title="E15">A6</font></i>: 
<span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c4">o1</font>
 <b>by </b><i><a class="txt" href="pralg_1.html#E5:12"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="pralg_1.html#E1:12_2"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/><a NAME="E6:12_2"/>
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>
 <b>by </b><i><a class="txt" href="pralg_1.html#E4:12"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="pralg_1.html#E5:12"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="pralg_1.html#E1:12_2"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c5">o12</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span> <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E8:12_2"/><i><font color="Green" title="E16">A7</font></i>: 
<span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c5">o12</font>
 <b>by </b><i><a class="txt" href="pralg_1.html#E4:12"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="pralg_1.html#E5:12"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="pralg_1.html#E1:12_2"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>;<br/> <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c2">U2</font></span>)</span>
<b>by </b><i><a class="txt" href="pralg_1.html#E1:12"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="unialg_2.html#D2" title="UNIALG_2:def.2">UNIALG_2:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font>
<b>by </b><i><a class="ref" href="unialg_1.html#D11" title="UNIALG_1:def.11">UNIALG_1:def 11</a></i>
;<br/><b>then reconsider </b><font color="Maroon" title="c6">o2</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> as   <a href="unialg_2.html#NM5" title="UNIALG_2:NM.5">operation</a> of <font color="Maroon" title="c2">U2</font> <b>by </b><i><a class="txt" href="pralg_1.html#E5:12"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="pralg_1.html#E1:12_2"><i><font color="Green" title="E13">A4</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E11:12_2"/>
( <font color="Maroon" title="c4">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">U1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> &amp; <font color="Maroon" title="c6">o2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c2">U2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> )
 ;<br/><b>hence </b><a NAME="E12:12_2"/>
<span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <span class="p2"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">n</font>
 <b>by </b><i><a class="txt" href="pralg_1.html#E1:12"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="pralg_1.html#E5:12"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="pralg_1.html#E2:12_2"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="pralg_1.html#E5:12_2"><i><font color="Green" title="E15">A6</font></i></a>, <a class="txt" href="pralg_1.html#E8:12_2"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="pralg_1.html#T6" target="_self" title="PRALG_1:th.6">Th6</a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:12"/><b>then </b>
 <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>
 
<b>by </b><i><a class="txt" href="pralg_1.html#E4:12"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="finseq_2.html#T10" title="FINSEQ_2:th.10">FINSEQ_2:10</a></i>;<br/>
<b>hence </b><a NAME="E8:12"/>
<span class="p1"><a href="pralg_1.html#K5" title="PRALG_1:func.5">[:</a><span class="default"><font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font></span><a href="pralg_1.html#K5" title="PRALG_1:func.5">:]</a></span>,<font color="Maroon" title="c1">U1</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> 
 <b>by </b><i><a class="ref" href="unialg_2.html#D2" title="UNIALG_2:def.2">UNIALG_2:def 2</a></i>;<br/>


</div>
