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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">c</font> &amp; <font color="Maroon" title="c2">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c1">a</font> implies <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:136"/><i><font color="Green" title="E66">A1</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">c</font>
 <b>and </b><br/><a NAME="E2:136"/><i><font color="Green" title="E67">A2</font></i>: 
<font color="Maroon" title="c2">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c1">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font></span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T41" title="XBOOLE_1:th.41">XBOOLE_1:41</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4" title="XBOOLE_1:th.4">XBOOLE_1:4</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">b</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">c</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c1">a</font></span>)</span>
<b>by </b><i><a class="txt" href="amistd_2.html#E2:136"><i><font color="Green" title="E67">A2</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">c</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T39" title="XBOOLE_1:th.39">XBOOLE_1:39</a></i>
<br/>.= 
<font color="Maroon" title="c3">c</font>
<b>by </b><i><a class="txt" href="amistd_2.html#E1:136"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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