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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">X</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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>, <font color="Olive" title="b4">q</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> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a>  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Olive" title="b4">q</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="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>, <font color="Olive" title="b3">q</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> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a>  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Olive" title="b3">q</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>, <font color="Olive" title="b2">q</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> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a>  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Olive" title="b2">q</font>,<font color="Maroon" title="c3">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">q</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> <a href="circcomb.html#R2" title="CIRCCOMB:pred.2">tolerates</a>  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font></span><br/>







<span class="kw">set </span><font color="Maroon" title="c6">S1</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">S2</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">A1</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">set </span><font color="Maroon" title="c9">A2</font> =  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font>;<br/>
<span class="kw">thus </span><a NAME="E1:99"/>
 <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a>  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T51" target="_self" title="CIRCCOMB:th.51">Th51</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="circcomb.html#D3" target="_self" title="CIRCCOMB:def.3">CIRCCOMB:def 3</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> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</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="c5">q</font>,<font color="Maroon" title="c3">f</font></span>)</span> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</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="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font></span>)</span> )</span><br/>

<a NAME="E2:99"/><span class="lab"><font color="Green" title="E51">A1</font></span>: 
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="c5">q</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="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c5">q</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" target="_self" title="CIRCCOMB:def.14">Def14</a></span>;<br/>
<a NAME="E3:99"/>
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="circcomb.html#K5" title="CIRCCOMB:func.5">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" target="_self" title="CIRCCOMB:def.14">Def14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:99"/>
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="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</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="c5">q</font>,<font color="Maroon" title="c3">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:99"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="ref" href="circcomb.html#T4" target="_self" title="CIRCCOMB:th.4">Th4</a></span>; <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#U4" title="MSUALG_1:sel.4">Charact</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="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font></span>)</span></span><br/>

<a NAME="E5:99"/><span class="lab"><font color="Green" title="E52">A2</font></span>: 
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font> <a href="funcop_1.html#K13" title="FUNCOP_1:func.13">.--&gt;</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T62" target="_self" title="CIRCCOMB:th.62">Th62</a></span>;<br/>
<a NAME="E6:99"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</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="c4">p</font>,<font color="Maroon" title="c3">f</font> <a href="funcop_1.html#K13" title="FUNCOP_1:func.13">.--&gt;</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T62" target="_self" title="CIRCCOMB:th.62">Th62</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:99"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</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="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircuit</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:99"><span class="lab"><font color="Green" title="E52">A2</font></span></a>, <a class="ref" href="circcomb.html#T4" target="_self" title="CIRCCOMB:th.4">Th4</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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