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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="circcomb.html#NM1">Gate</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>4</sub></font> being   <a href="circcomb.html#NM1">Gate</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>assume </b><a NAME="E2:22"/>
(  not <font color="Maroon">c<sub>1</sub></font> is <a href="msualg_1.html#V2">void</a> or  not <font color="Maroon">c<sub>2</sub></font> is <a href="msualg_1.html#V2">void</a> )
 ;<br/>

<a NAME="E3:22"/><b>then </b>
( ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> ) &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" target="_self">Def2</a>, <a class="txt" href="circcomb.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:22"/>
the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="circcomb.html#K3" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_1.html#D5">MSUALG_1:def 5</a><br/>


</div>
