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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="prob_1.html#M2">Event</a> of  <a href="prob_1.html#K14">Borel_Sets</a> ;<br/>



<b>assume </b><a NAME="E1:10"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_1_1"/>
( ( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> ) or ( not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> ) or ( not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> ) )
 </span><b>by </b><i><a class="txt" href="qmax_1.html#E1:10"><i><font color="Green">E7</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_1"><b>suppose </b></a><a NAME="E1:10_1_1_1"/><i><font color="Green">E8</font></i>: 
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><div class="add"><a NAME="E2:10_1_1_1"/><b>then </b><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="txt" href="qmax_1.html#E8"><i><font color="Green">Lemma3</font></i></a></i>;<br/><a NAME="E3:10_1_1_1"/>
0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="qmax_1.html#E1:10_1_1_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E4:10_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="qmax_1.html#E2:10_1_1_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="qmax_1.html#E8"><i><font color="Green">Lemma3</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_2"><b>suppose </b></a><a NAME="E1:10_1_1_2"/><i><font color="Green">E8</font></i>: 
( not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><div class="add"><a NAME="E2:10_1_1_2"/><b>then </b><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="txt" href="qmax_1.html#E8"><i><font color="Green">Lemma3</font></i></a></i>;<br/><a NAME="E3:10_1_1_2"/>
0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="qmax_1.html#E1:10_1_1_2"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E4:10_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="qmax_1.html#E2:10_1_1_2"><i><font color="Green">E9</font></i></a>, <a class="txt" href="qmax_1.html#E8"><i><font color="Green">Lemma3</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_3"><b>suppose </b></a><a NAME="E1:10_1_1_3"/><i><font color="Green">E8</font></i>: 
( not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><div class="add"><a NAME="E2:10_1_1_3"/><b>then </b><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="txt" href="qmax_1.html#E8"><i><font color="Green">Lemma3</font></i></a></i>;<br/><a NAME="E3:10_1_1_3"/>
not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="qmax_1.html#E1:10_1_1_3"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E4:10_1_1_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="qmax_1.html#E2:10_1_1_3"><i><font color="Green">E9</font></i></a>, <a class="txt" href="qmax_1.html#E8"><i><font color="Green">Lemma3</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:10"/>
<font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>


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