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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:35_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:35_1_1"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E5:35_1_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="pscomp_1.html#E3:35_1_1"><i><font color="Green">E24</font></i></a></i>;<br/><a NAME="E6:35_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E3:35_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="pscomp_1.html#E5:35_1_1"><i><font color="Green">E25</font></i></a></i>;<br/><b>hence </b><a NAME="E7:35_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E5:35_1_1"><i><font color="Green">E25</font></i></a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:35_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:35_1"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/><a NAME="E5:35_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E4:35_1"><i><font color="Green">E24</font></i></a></i>;<br/><a NAME="E6:35_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="real_1.html#K3">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><b>hence </b><a NAME="E7:35_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="pscomp_1.html#E4:35_1"><i><font color="Green">E24</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:35"/>
<font color="Maroon">c<sub>2</sub></font> <a href="measure6.html#K6">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</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="real_1.html#K3">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="measure6.html#K6">+</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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