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<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  not <font color="Maroon" title="c1">S1</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> or  not <font color="Maroon" title="c2">S2</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> ) implies  not <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> )</span><br/>

<b>consider </b><font color="Maroon" title="c3">o1</font> being   <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c4">o2</font> being   <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Maroon" title="c2">S2</font>;<br/>
<a NAME="E2:21"/><i><font color="Green" title="E12">Lm2</font></i>: 
for <font color="Olive" title="b1">S</font> being non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/> for <font color="Olive" title="b2">o</font> being  <a href="circcomb.html#NM1" title="CIRCCOMB:NM.1">Gate</a> of <font color="Olive" title="b1">S</font> holds  <font color="Olive" title="b2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">S</font>
 
;<br/>
<b>assume </b><a NAME="E3:21"/>
(  not <font color="Maroon" title="c1">S1</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> or  not <font color="Maroon" title="c2">S2</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a></span><br/>

<a NAME="E4:21"/><b>then </b>
( ( <font color="Maroon" title="c3">o1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> or <font color="Maroon" title="c4">o2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> ) &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" target="_self" title="CIRCCOMB:def.2">Def2</a>, <a class="txt" href="#E2:21"><i><font color="Green" title="E12">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:21"/>
not the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D13" title="STRUCT_0:def.13">STRUCT_0:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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