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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <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"> ( <font color="Maroon" title="c1">S</font> is  <a href="circcmb3.html#V4" title="CIRCCMB3:attr.4">one-gate</a>  implies ( <font color="Maroon" title="c1">S</font> is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  &amp; not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp; not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="circcomb.html#V1" title="CIRCCOMB:attr.1">unsplit</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="circcomb.html#V2" title="CIRCCOMB:attr.2">gate`1=arity</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:24_1_1"/>
<font color="Maroon" title="c1">S</font> is  <a href="circcmb3.html#V4" title="CIRCCMB3:attr.4">one-gate</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">S</font> is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  &amp; not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp; not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="circcomb.html#V1" title="CIRCCOMB:attr.1">unsplit</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="circcomb.html#V2" title="CIRCCOMB:attr.2">gate`1=arity</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>  )</span><br/>

<a NAME="E2:24_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">X</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ex <font color="Olive" title="b2">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ex <font color="Olive" title="b3">p</font> being  <a href="circcomb.html#NM2" title="CIRCCOMB:NM.2">FinSeqLen</a> of <font color="Olive" title="b2">n</font> ex <font color="Olive" title="b4">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Olive" title="b1">X</font></span>)</span>,<font color="Olive" title="b1">X</font> st <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcmb3.html#D6" target="_self" title="CIRCCMB3:def.6">Def6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:24_1_1"/>
( <font color="Maroon" title="c1">S</font> is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  &amp; not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp; not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="circcomb.html#V1" title="CIRCCOMB:attr.1">unsplit</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="circcomb.html#V2" title="CIRCCOMB:attr.2">gate`1=arity</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</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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