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<span class="kw">set </span><font color="Maroon" title="c1">X</font> =  <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c2">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">p</font> being  <a href="circcomb.html#NM2" title="CIRCCOMB:NM.2">FinSeqLen</a> of <font color="Maroon" title="c2">n</font><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="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  holds   <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">f</font> is  <a href="circcomb.html#V3" title="CIRCCOMB:attr.3">gate`2isBoolean</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="c2">n</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">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="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  holds   <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">p</font>,<font color="Olive" title="b1">f</font> is  <a href="circcomb.html#V3" title="CIRCCOMB:attr.3">gate`2isBoolean</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">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="c2">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ; <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#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">f</font> is  <a href="circcomb.html#V3" title="CIRCCOMB:attr.3">gate`2isBoolean</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">g</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="circcomb.html#D9" target="_self" title="CIRCCOMB:def.9">CIRCCOMB:def 9</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="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">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="c4">f</font></span>)</span> implies for <font color="Olive" title="b1">p</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</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="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">g</font> holds <br/> ex <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<font color="Olive" title="b2">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/>







<a NAME="E1:93"/><span class="lab"><font color="Green" title="E50">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D18" title="FINSEQ_1:def.18">FINSEQ_1:def 18</a></span>;<br/>
<a NAME="E2:93"/><span class="lab"><font color="Green" title="E51">A2</font></span>: 
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</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="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#D6" target="_self" title="CIRCCOMB:def.6">Def6</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:93"/>
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">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="c4">f</font></span>)</span>
 ; <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="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</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="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">g</font> holds <br/> ex <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">p</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<font color="Olive" title="b2">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>

<a NAME="E4:93"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A3</font></span>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T48" target="_self" title="CIRCCOMB:th.48">Th48</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">q</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</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="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">g</font> implies  ex <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">q</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<font color="Olive" title="b1">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E5:93"/>
<font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</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="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">g</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <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"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">q</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  st <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<font color="Olive" title="b1">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c4">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">q</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span>)</span>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="txt" href="#E2:93"><span class="lab"><font color="Green" title="E51">A2</font></span></a>, <a class="txt" href="#E1:93"><span class="lab"><font color="Green" title="E50">A1</font></span></a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c7">f</font>
; <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="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<font color="Maroon" title="c7">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><br/>

<span class="kw">thus </span><a NAME="E7:93"/>
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<font color="Maroon" title="c7">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:93"><span class="lab"><font color="Green" title="E52">A3</font></span></a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</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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