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<div><span class="kw">theorem </span><a NAME="T14"><span class="comment"><font color="firebrick">:: FACIRC_2:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds   <a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="facirc_2.html#K3" title="FACIRC_2:func.3">-BitAdderStr</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msafree2.html#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="facirc_2.html#K3" title="FACIRC_2:func.3">-BitAdderStr</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">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#K3" title="MSAFREE2:func.3">InnerVertices</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K19" title="FACIRC_1:func.19">BitAdderWithOverflowStr</a> (<span class="p3">(<span class="default"><font color="Olive" title="b2">x</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">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="b3">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">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="b1">n</font> <a href="facirc_2.html#K5" title="FACIRC_2:func.5">-BitMajorityOutput</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b3">y</font>)</span>)</span>)</span>)</span></span>)</span></div></div>
