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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: RADIX_4:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">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> 2 holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="radix_3.html#K7" title="RADIX_3:func.7">DigA_SDSub</a> (<span class="p2">(<span class="default"><a href="radix_3.html#K10" title="RADIX_3:func.10">SD2SDSub</a> <span class="p3">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Olive" title="b2">x</font>,<span class="p4">(<span class="default"><font color="Olive" title="b3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Olive" title="b2">x</font>,<span class="p5">(<span class="default"><font color="Olive" title="b3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span>,<span class="p4">(<span class="default"><font color="Olive" title="b3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p4">(<span class="default"><font color="Olive" title="b3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="radix_3.html#K5" title="RADIX_3:func.5">SDSub_Add_Carry</a> (<span class="p4">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p5">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Olive" title="b2">x</font>,<span class="p0">(<span class="default"><font color="Olive" title="b3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span>,<span class="p5">(<span class="default"><font color="Olive" title="b3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>)</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <font color="Olive" title="b1">k</font></span>)</span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="radix_3.html#K5" title="RADIX_3:func.5">SDSub_Add_Carry</a> (<span class="p3">(<span class="default"><a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<span class="p4">(<span class="default"><a href="radix_1.html#K10" title="RADIX_1:func.10">DecSD</a> (<font color="Olive" title="b2">x</font>,<span class="p5">(<span class="default"><font color="Olive" title="b3">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span>,<font color="Olive" title="b3">n</font>)</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span></span>)</span></div></div>
