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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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 <span class="p1">(<span class="default"><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#K8" title="CIRCCOMB:func.8">BOOLEAN</a> </span>)</span>,<a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a> <br/> for <font color="Olive" title="b2">p</font> being  <a href="circcomb.html#NM2" title="CIRCCOMB:NM.2">FinSeqLen</a> of <font color="Maroon" title="c1">n</font> holds   <a href="circcomb.html#K7" title="CIRCCOMB:func.7">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/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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#K8" title="CIRCCOMB:func.8">BOOLEAN</a> </span>)</span>,<a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="circcomb.html#NM2" title="CIRCCOMB:NM.2">FinSeqLen</a> of <font color="Maroon" title="c1">n</font> holds   <a href="circcomb.html#K7" title="CIRCCOMB:func.7">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/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="circcomb.html#NM2" title="CIRCCOMB:NM.2">FinSeqLen</a> of <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">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/>





<span class="kw">set </span><font color="Maroon" title="c4">S</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">A</font> =  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font>;<br/>
<span class="kw">let </span><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#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">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#K8" title="CIRCCOMB:func.8">BOOLEAN</a> </span><br/>

<a NAME="E1:109"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">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#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c2">f</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <a href="circcomb.html#K8" title="CIRCCOMB:func.8">BOOLEAN</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D14" target="_self" title="CIRCCOMB:def.14">Def14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:109"/>
the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">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#K8" title="CIRCCOMB:func.8">BOOLEAN</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>; <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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