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<div><div><a NAME="S14"><span class="kw">scheme  </span><span class="comment"><font color="firebrick">:: CIRCCMB3:sch 14</font></span><br/></a><span class="lab"><font color="Green" title="E14">Comb1CircResult</font></span>{ <font color="Maroon">F<sub>1</sub></font>() <span class="kw">-&gt; </span>   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> , <font color="Maroon">F<sub>2</sub></font>() <span class="kw">-&gt; </span>  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#M2" title="HIDDEN:mode.2">set</a> , <font color="Maroon">F<sub>3</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>(), <font color="Maroon">F<sub>4</sub></font>() <span class="kw">-&gt; </span>  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="circcmb3.html#M1" title="CIRCCMB3:mode.1">Signature</a> of <font color="Maroon">F<sub>2</sub></font>(), <font color="Maroon">F<sub>5</sub></font>() <span class="kw">-&gt; </span>   <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>4</sub></font>(), <font color="Maroon">F<sub>6</sub></font>() <span class="kw">-&gt; </span>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default">1 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span>,<font color="Maroon">F<sub>2</sub></font>() } :<br/><div class="add"><a NAME="E3:93"/>
 for <font color="Olive" title="b1">s</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><font color="Maroon">F<sub>5</sub></font>() <a href="circcmb3.html#K7" title="CIRCCMB3:func.7">+*</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K5" title="CIRCCMB3:func.5">1GateCircuit</a> (<span class="p3"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>())</span>)</span></span>)</span><br/>  for <font color="Olive" title="b2">s9</font> being   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon">F<sub>5</sub></font>()  st <font color="Olive" title="b2">s9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="relat_1.html#K5" title="RELAT_1:func.5">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>4</sub></font>() holds <br/> for <font color="Olive" title="b3">a1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st ( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Olive" title="b3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Olive" title="b2">s9</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) &amp; (  not <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <font color="Maroon">F<sub>4</sub></font>() implies <font color="Olive" title="b3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>1</sub></font>() ) holds <br/><span class="p1">(<span class="default"><a href="circcmb3.html#K1" title="CIRCCMB3:func.1">Result</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K3" title="CIRCCMB3:func.3">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K4" title="CIRCCMB3:func.4">1GateCircStr</a> (<span class="p3"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>())</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b3">a1</font>)
 </div><span class="kw">provided</span><div class="add"><a NAME="E1:93"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
 for <font color="Olive" title="b1">g</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default">1 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon">F<sub>2</sub></font>()</span>)</span>,<font color="Maroon">F<sub>2</sub></font>() holds <br/> ( <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon">F<sub>6</sub></font>() iff  for <font color="Olive" title="b2">a1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Olive" title="b1">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b2">a1</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b2">a1</font>) )
 <span class="kw">and </span><br/><a NAME="E2:93"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
 not  <a href="circcmb3.html#K3" title="CIRCCMB3:func.3">Output</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K4" title="CIRCCMB3:func.4">1GateCircStr</a> (<span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>()</span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>())</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <font color="Maroon">F<sub>4</sub></font>()
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