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<span class="kw">let </span><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">b</font> be  non  <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</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">  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K40" title="TWOSCOMP:func.40">BitCompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">S1</font> =  <a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">S2</font> =  <a href="twoscomp.html#K37" title="TWOSCOMP:func.37">IncrementStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">S</font> =  <a href="twoscomp.html#K40" title="TWOSCOMP:func.40">BitCompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font>;<br/>
<a NAME="E1:61"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
(  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K37" title="TWOSCOMP:func.37">IncrementStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T40" title="FACIRC_1:th.40">FACIRC_1:40</a></span>;<br/>
<a NAME="E2:61"/>
(  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K34" title="TWOSCOMP:func.34">CompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> &amp;  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K37" title="TWOSCOMP:func.37">IncrementStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="facirc_1.html#T38" title="FACIRC_1:th.38">FACIRC_1:38</a></span>;<br/>
<span class="kw">then </span> <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K40" title="TWOSCOMP:func.40">BitCompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> = 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="ref" href="facirc_1.html#T7" title="FACIRC_1:th.7">FACIRC_1:7</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>

;<br/>
<span class="kw">hence </span><a NAME="E4:61"/>
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="twoscomp.html#K40" title="TWOSCOMP:func.40">BitCompStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</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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