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<b>assume </b><a NAME="E1:10_1"/><i><font color="Green">E2</font></i>: 
( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] or ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">P<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 ;<br/>

<div><i><font color="Green">E3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>1</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E1:10_1_1"/><i><font color="Green">E4</font></i>: 
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">c<sub>1</sub></font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:10_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:10_1_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] &amp; <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">c<sub>1</sub></font>] )
 <b>by </b><i><a class="txt" href="schems_1.html#E1:10"><i><font color="Green">E1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:10_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="schems_1.html#E1:10_1_1"><i><font color="Green">E4</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:10_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:10_1_2"/><i><font color="Green">E4</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:10_1_2_1"/><i><font color="Green">E5</font></i>: 
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>] &amp; <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">c<sub>1</sub></font>] )
 <b>by </b><i><a class="txt" href="schems_1.html#E1:10"><i><font color="Green">E1</font></i></a></i>;<br/><b>thus </b><a NAME="E3:10_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="schems_1.html#E1:10_1_2"><i><font color="Green">E4</font></i></a>, <a class="txt" href="schems_1.html#E2:10_1_2_1"><i><font color="Green">E5</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:10_1_2"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="schems_1.html#E1:10_1"><i><font color="Green">E2</font></i></a>, <a class="txt" href="schems_1.html#E2:10_1"><i><font color="Green">E3</font></i></a></i>;<br/>


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