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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="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:8"/>
( <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K5">\+\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K5">\+\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_5.html#K1" target="_self">proj1</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_5.html#K2" target="_self">proj2</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_5.html#K1" target="_self">proj1</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_5.html#K2" target="_self">proj2</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_5.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E2:8"/><b>then </b>
( <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K5">\+\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K5">\+\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K1" target="_self">proj1</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K2" target="_self">proj2</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_5.html#T6" target="_self">Th6</a>, <a class="ref" href="xboole_1.html#T13">XBOOLE_1:13</a></i>;<br/>
<b>hence </b><a NAME="E3:8"/>
( <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K5">\+\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K1" target="_self">proj1</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_5.html#K1" target="_self">proj1</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K5">\+\</a> <span class="p1">(<span class="default"><a href="funct_5.html#K2" target="_self">proj2</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_5.html#K2" target="_self">proj2</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K5">\+\</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/>


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