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<b>let </b><font color="Maroon" title="c3">i1</font>, <font color="Maroon" title="c4">i2</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">Omega</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c3">i1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dynkin.html#K5" title="DYNKIN:func.5">disjointify</a> <font color="Maroon" title="c2">g</font>,<font color="Olive" title="b1">n</font> ) &amp; ( for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c4">i2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dynkin.html#K5" title="DYNKIN:func.5">disjointify</a> <font color="Maroon" title="c2">g</font>,<font color="Olive" title="b1">n</font> ) implies <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> )</span><br/>

<b>assume </b><a NAME="E1:15_1_2"/><i><font color="Green" title="E9">A2</font></i>: 
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c3">i1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dynkin.html#K5" title="DYNKIN:func.5">disjointify</a> <font color="Maroon" title="c2">g</font>,<font color="Olive" title="b1">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st not <font color="Maroon" title="c4">i2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dynkin.html#K5" title="DYNKIN:func.5">disjointify</a> <font color="Maroon" title="c2">g</font>,<font color="Olive" title="b1">n</font> or <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> )</span><br/>

<b>assume </b><a NAME="E2:15_1_2"/><i><font color="Green" title="E10">A3</font></i>: 
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c4">i2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dynkin.html#K5" title="DYNKIN:func.5">disjointify</a> <font color="Maroon" title="c2">g</font>,<font color="Olive" title="b1">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">n</font> be    <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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">i1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font></span><br/><a NAME="E1:15_1_2_1"/>
( <font color="Maroon" title="c3">i1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dynkin.html#K5" title="DYNKIN:func.5">disjointify</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c5">n</font> &amp; <font color="Maroon" title="c4">i2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="dynkin.html#K5" title="DYNKIN:func.5">disjointify</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c5">n</font> )
 <b>by </b><i><a class="txt" href="dynkin.html#E1:15_1_2"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="dynkin.html#E2:15_1_2"><i><font color="Green" title="E10">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E2:15_1_2_1"/>
<font color="Maroon" title="c3">i1</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">i2</font> <a href="prob_1.html#K1" title="PROB_1:func.1">.</a> <font color="Maroon" title="c5">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15_1_2"/>
<font color="Maroon" title="c3">i1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">i2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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