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<span class="kw">let </span><font color="Maroon" title="c1">f</font> be    <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">p</font>, <font color="Olive" title="b2">q</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds   <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Olive" title="b1">p</font>,<font color="Maroon" title="c1">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="Olive" title="b2">q</font>,<font color="Maroon" title="c1">f</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">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">  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">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="c3">q</font>,<font color="Maroon" title="c1">f</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c4">S1</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">S2</font> =  <a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">f</font>;<br/>
<a NAME="E1:68"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> implies <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T17" title="ZFMISC_1:th.17">ZFMISC_1:17</a></span>;<br/>
<a NAME="E2:68"/><span class="lab"><font color="Green" title="E37">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">q</font>,<font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">f</font> <a href="funcop_1.html#K13" title="FUNCOP_1:func.13">.--&gt;</a> <font color="Maroon" title="c3">q</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T47" target="_self" title="CIRCCOMB:th.47">Th47</a></span>;<br/>
<a NAME="E3:68"/>
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="c2">p</font>,<font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font> <a href="funcop_1.html#K13" title="FUNCOP_1:func.13">.--&gt;</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcomb.html#T47" target="_self" title="CIRCCOMB:th.47">Th47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:68"/>
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="c2">p</font>,<font color="Maroon" title="c1">f</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</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">q</font>,<font color="Maroon" title="c1">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E1:68"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="ref" href="circcomb.html#T4" target="_self" title="CIRCCOMB:th.4">Th4</a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="circcomb.html#D1" target="_self" title="CIRCCOMB:def.1">CIRCCOMB:def 1</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#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">f</font></span>)</span></span><br/>

<a NAME="E5:68"/><span class="lab"><font color="Green" title="E38">A3</font></span>: 
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">f</font> <a href="funcop_1.html#K13" title="FUNCOP_1:func.13">.--&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">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#T47" target="_self" title="CIRCCOMB:th.47">Th47</a></span>;<br/>
<a NAME="E6:68"/>
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font> <a href="funcop_1.html#K13" title="FUNCOP_1:func.13">.--&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">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#T47" target="_self" title="CIRCCOMB:th.47">Th47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:68"/>
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c1">f</font></span>)</span> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K5" title="CIRCCOMB:func.5">1GateCircStr</a> <font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c1">f</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:68"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="txt" href="#E1:68"><span class="lab"><font color="Green" title="E36">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"> verum</span><br/>


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