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<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#NM1" title="UNIALG_1:NM.1">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="E1:5"/>
( <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="firebrick">::  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="E2:5"/><span class="kw">then </span>
(  <a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c1">U1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c2">U2</font> &amp;  <a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c2">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="unialg_1.html#K1" title="UNIALG_1:func.1">signature</a> <font color="Maroon" title="c3">U3</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="unialg_2.html#D1" target="_self" title="UNIALG_2:def.1">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:5"/>
<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#D1" target="_self" title="UNIALG_2:def.1">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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