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<span class="kw">let </span><font color="Maroon" title="c4">k1</font>, <font color="Maroon" title="c5">k2</font> be   <a href="finseq_2.html#NM4" title="FINSEQ_2:NM.4">Tuple</a> of <font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">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="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> holds <br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<font color="Maroon" title="c4">k1</font>,<font color="Olive" title="b1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> (<font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">k</font>) ) &amp; (  for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> holds <br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<font color="Maroon" title="c5">k2</font>,<font color="Olive" title="b1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> (<font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">k</font>) ) implies <font color="Maroon" title="c4">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28_1_2"/><span class="lab"><font color="Green" title="E18">A5</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> holds <br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<font color="Maroon" title="c4">k1</font>,<font color="Olive" title="b1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> (<font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">k</font>)
 <span class="kw">and </span><br/><a NAME="E2:28_1_2"/><span class="lab"><font color="Green" title="E19">A6</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> holds <br/> <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<font color="Maroon" title="c5">k2</font>,<font color="Olive" title="b1">i</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> (<font color="Maroon" title="c3">x</font>,<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c1">k</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font></span><br/>

<a NAME="E3:28_1_2"/><span class="lab"><font color="Green" title="E20">A7</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/>
<a NAME="E4:28_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A8</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E22">A9</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">j</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="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">k1</font> implies <font color="Maroon" title="c4">k1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> )</span><br/><span class="kw">assume </span><a NAME="E1:28_1_2_1"/><span class="lab"><font color="Green" title="E23">A10</font></span>: 
<font color="Maroon" title="c6">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">k1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">k1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font></span><br/><span class="kw">then </span><font color="Maroon" title="c4">k1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> = 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<font color="Maroon" title="c4">k1</font>,<font color="Maroon" title="c6">j</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28_1_2"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="ref" href="radix_1.html#D3" target="_self" title="RADIX_1:def.3">Def3</a></span>
<br/>.= 
 <a href="radix_1.html#K9" title="RADIX_1:func.9">DigitDC</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c6">j</font>,<font color="Maroon" title="c1">k</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28_1_2"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="txt" href="#E4:28_1_2"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E1:28_1_2_1"><span class="lab"><font color="Green" title="E23">A10</font></span></a></span>
<br/>.= 
 <a href="radix_1.html#K4" title="RADIX_1:func.4">DigA</a> (<font color="Maroon" title="c5">k2</font>,<font color="Maroon" title="c6">j</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28_1_2"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E4:28_1_2"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E1:28_1_2_1"><span class="lab"><font color="Green" title="E23">A10</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c5">k2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28_1_2"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E1:28_1_2_1"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="ref" href="radix_1.html#D3" target="_self" title="RADIX_1:def.3">Def3</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:28_1_2_1"/>
<font color="Maroon" title="c4">k1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">j</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E6:28_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#D7" title="CARD_1:def.7">CARD_1:def 7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:28_1_2"/>
<font color="Maroon" title="c4">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">k2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28_1_2"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E5:28_1_2"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="finseq_2.html#T9" title="FINSEQ_2:th.9">FINSEQ_2:9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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