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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1;<br/>
<a NAME="E1:109"/><i><font color="Green">E86</font></i>: 
<span class="p1">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R2">in</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<a NAME="E2:109"/><i><font color="Green">E87</font></i>: 
(  <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T17">XXREAL_0:17</a></i>;<br/>
<a NAME="E3:109"/><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T148">XREAL_1:148</a></i>;<br/>
<a NAME="E4:109"/><b>then </b>
( <span class="p1">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E2:109"><i><font color="Green">E87</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E5:109"/><b>then </b><i><font color="Green">E89</font></i>: 
not <span class="p1">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_5.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E6:109"/>
not <span class="p1">(<span class="default"><a href="xxreal_0.html#K3">min</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R2">in</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="borsuk_5.html#E2:109"><i><font color="Green">E87</font></i></a>, <a class="txt" href="borsuk_5.html#E3:109"><i><font color="Green">E88</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:109"/>
<span class="p1"><a href="borsuk_5.html#NK3" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="borsuk_5.html#NK3" target="_self">,+infty.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="numbers.html#K1">REAL</a> 
 <b>by </b><i><a class="txt" href="borsuk_5.html#E1:109"><i><font color="Green">E86</font></i></a>, <a class="txt" href="borsuk_5.html#E5:109"><i><font color="Green">E89</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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