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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <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> ; <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">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> <br/> for <font color="Olive" title="b2">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> <font color="Olive" title="b1">X</font></span>)</span>,<font color="Olive" title="b1">X</font><br/> for <font color="Olive" title="b3">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="b3">p</font>,<font color="Olive" title="b2">f</font> is    <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Olive" title="b1">X</font>, <a href="circcmb3.html#K4" title="CIRCCMB3:func.4">1GateCircStr</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b2">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be  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> ; <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> <font color="Maroon" title="c2">X</font></span>)</span>,<font color="Maroon" title="c2">X</font><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="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c2">X</font>, <a href="circcmb3.html#K4" title="CIRCCMB3:func.4">1GateCircStr</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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> <font color="Maroon" title="c2">X</font></span>)</span>,<font color="Maroon" title="c2">X</font>; <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="c3">f</font> is    <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c2">X</font>, <a href="circcmb3.html#K4" title="CIRCCMB3:func.4">1GateCircStr</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c3">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="c4">p</font>,<font color="Maroon" title="c3">f</font> is    <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c2">X</font>, <a href="circcmb3.html#K4" title="CIRCCMB3:func.4">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span><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="c4">p</font>,<font color="Maroon" title="c3">f</font>;<br/>
<span class="kw">thus </span><a NAME="E1:56"/>
 <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font> is  <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="circcmb3.html#D10" target="_self" title="CIRCCMB3:def.10">CIRCCMB3:def 10</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="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp;  <a href="funct_1.html#K3" title="FUNCT_1:func.3">the_value_of</a> 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="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> )</span><br/>

<a NAME="E2:56"/>
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="c4">p</font>,<font color="Maroon" title="c3">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="circcmb3.html#K4" title="CIRCCMB3:func.4">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D14" title="CIRCCOMB:def.14">CIRCCOMB:def 14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:56"/>
( 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="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp;  <a href="funct_1.html#K3" title="FUNCT_1:func.3">the_value_of</a> 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="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">X</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T94" title="FUNCOP_1:th.94">FUNCOP_1:94</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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