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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds   <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span>)</span></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span></span><br/>



<b>set </b><font color="Maroon" title="c4">Sn</font> = <font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>;<br/>
<b>set </b><font color="Maroon" title="c5">SSn</font> =  <a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span>;<br/>
<a NAME="E1:33"/>
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T27" title="FACIRC_1:th.27">FACIRC_1:27</a></i>;<br/>
<b>hence </b><a NAME="E2:33"/>
 <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c3">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="gfacirc2.html#T21" target="_self" title="GFACIRC2:th.21">Th21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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