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<span class="kw">let </span><font color="Maroon" title="c1">n</font>, <font color="Maroon" title="c2">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font> being  <a href="finseq_2.html#NM4" title="FINSEQ_2:NM.4">Tuple</a> of <font color="Maroon" title="c1">n</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">y</font> being  <a href="finseq_2.html#NM4" title="FINSEQ_2:NM.4">Tuple</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/> <a href="radix_2.html#K3" title="RADIX_2:func.3">SDDec2</a> <font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Olive" title="b2">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be   <a href="finseq_2.html#NM4" title="FINSEQ_2:NM.4">Tuple</a> of <font color="Maroon" title="c1">n</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">y</font> being  <a href="finseq_2.html#NM4" title="FINSEQ_2:NM.4">Tuple</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a>   st <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> holds <br/> <a href="radix_2.html#K3" title="RADIX_2:func.3">SDDec2</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Olive" title="b1">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">y</font> be   <a href="finseq_2.html#NM4" title="FINSEQ_2:NM.4">Tuple</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">k</font> <a href="radix_1.html#K3" title="RADIX_1:func.3">-SD</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> implies  <a href="radix_2.html#K3" title="RADIX_2:func.3">SDDec2</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c4">y</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:18"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="radix_2.html#K3" title="RADIX_2:func.3">SDDec2</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c4">y</font></span><br/>

<a NAME="E2:18"/><span class="kw">then </span>
 <a href="radix_2.html#K3" title="RADIX_2:func.3">SDDec2</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gr_cy_1.html#K1" title="GR_CY_1:func.1">Sum</a> <span class="p1">(<span class="default"><a href="radix_1.html#K7" title="RADIX_1:func.7">DigitSD</a> <font color="Maroon" title="c4">y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="radix_2.html#T12" target="_self" title="RADIX_2:th.12">Th12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:18"/>
 <a href="radix_2.html#K3" title="RADIX_2:func.3">SDDec2</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K8" title="RADIX_1:func.8">SDDec</a> <font color="Maroon" title="c4">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="radix_1.html#D7" title="RADIX_1:def.7">RADIX_1:def 7</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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