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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  )</span><br/>

<span class="kw">consider </span><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/>
<span class="kw">assume </span><a NAME="E2:23"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
(  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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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="E3:23"/>
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#K2" title="CIRCCOMB:func.2">+*</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D2" target="_self" title="CIRCCOMB:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:23"/>
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#K2" title="CIRCCOMB:func.2">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:23"><span class="lab"><font color="Green" title="E11">A1</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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