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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E23">Def8</font></span>   defines <a href="gfacirc2.html#K8" title="GFACIRC2:func.8">-BitGFA1AdderOutput</a> <a onclick="hs(this)" href="javascript:()">GFACIRC2:def 8 : <br/></a><span> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">n</font> holds <br/> for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive">b<sub>5</sub></font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">n</font> <a href="gfacirc2.html#K5" title="GFACIRC2:func.5">-BitGFA1Str</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span> holds <br/> ( <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Olive" title="b1">k</font>,<font color="Olive" title="b2">n</font>) <a href="gfacirc2.html#K8" title="GFACIRC2:func.8">-BitGFA1AdderOutput</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) iff  ex <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</a> (<span class="p1">(<span class="default"><font color="Olive" title="b3">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b6">i</font> <a href="gfacirc2.html#K7" title="GFACIRC2:func.7">-BitGFA1CarryOutput</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span>) ) );<br/></span></div>
