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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> , <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> <br/> for <font color="Olive" title="b2">p</font> being   <a href="circcomb.html#M1" title="CIRCCOMB:mode.1">FinSeqLen</a> of <font color="Maroon" title="c1">n</font> holds   <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> , <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being   <a href="circcomb.html#M1" title="CIRCCOMB:mode.1">FinSeqLen</a> of <font color="Maroon" title="c1">n</font> holds   <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c2">f</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a></span><br/><b>let </b><font color="Maroon" title="c3">p</font> be    <a href="circcomb.html#M1" title="CIRCCOMB:mode.1">FinSeqLen</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font> is <a href="circcomb.html#V6" title="CIRCCOMB:attr.6">Boolean</a></span><br/>





<b>set </b><font color="Maroon" title="c4">S</font> =  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircStr</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font>;<br/>
<b>set </b><font color="Maroon" title="c5">A</font> =  <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font>;<br/>
<a NAME="E1:109"/><i><font color="Green" title="E61">A1</font></i>: 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircStr</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> 
 
<b>by </b><i><a class="ref" href="circcomb.html#D14" target="_self" title="CIRCCOMB:def.14">Def14</a></i>;<br/>
<b>let </b><font color="Maroon" title="c6">v</font> be   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircStr</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D15" target="_self" title="CIRCCOMB:def.15">CIRCCOMB:def 15</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> </span><br/>

<b>thus </b><a NAME="E2:109"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> 
 <b>by </b><i><a class="txt" href="circcomb.html#E1:109"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>; <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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