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<b>let </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>;<br/>

<b>assume </b><a NAME="E1:152_1_2"/><i><font color="Green" title="E62">A6</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">p</font> &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">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#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">p</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c2">x1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>] ) &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">p</font> &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">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#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">p</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">i</font>,<font color="Maroon" title="c3">x2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font>] ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="152_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:152_1_2_1"/>
<font color="Maroon" title="c4">k</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="c1">p</font>
 ;<br/><a NAME="E2:152_1_2_1"/><b>then </b>
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c2">x1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">k</font>,<font color="Maroon" title="c3">x2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font>] )
 <b>by </b><i><a class="txt" href="trees_3.html#E1:152_1_2"><i><font color="Green" title="E62">A6</font></i></a></i>;<br/><b>hence </b><a NAME="E3:152_1_2_1"/>
<font color="Maroon" title="c2">x1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">k</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:152_1_2"/>
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font>
 <b>by </b><i><a class="txt" href="trees_3.html#E1:152_1_2"><i><font color="Green" title="E62">A6</font></i></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>;<br/>


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