<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font>, <font color="Maroon" title="c3">U3</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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>  &amp; <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c3">U3</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  implies <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:9"/>
( <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>  &amp; <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c3">U3</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> </span><br/>

<a NAME="E2:9"/><span class="kw">then </span>
(  <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> <font color="Maroon" title="c2">U2</font> &amp;  <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K4" title="UNIALG_1:func.4">signature</a> <font color="Maroon" title="c3">U3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D2" target="_self" title="UNIALG_2:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:9"/>
<font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c3">U3</font> <a href="unialg_2.html#R1" title="UNIALG_2:pred.1">are_similar</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D2" target="_self" title="UNIALG_2:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
