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<div><span class="kw">theorem </span><a NAME="T10"><span class="comment"><font color="firebrick">:: FSCIRC_2:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">k</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>   st <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">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> holds  (<span class="p1">(<span class="default"><font color="Olive" title="b2">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b1">n</font>) <a href="fscirc_2.html#K4" title="FSCIRC_2:func.4">-BitSubtracterOutput</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="fscirc_1.html#K1" title="FSCIRC_1:func.1">BitSubtracterOutput</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> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b4">y</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b2">k</font> <a href="fscirc_2.html#K3" title="FSCIRC_2:func.3">-BitBorrowOutput</a> (<font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font>)</span>)</span>)</div></div>
