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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>  st <font color="Olive" title="b1">x</font> <a href="waybel_4.html#R3" title="WAYBEL_4:pred.3">is_maximal_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Olive" title="b2">y</font></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Olive" title="b2">y</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="waybel_4.html#R3" title="WAYBEL_4:pred.3">is_maximal_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span> implies <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:3"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="waybel_4.html#R3" title="WAYBEL_4:pred.3">is_maximal_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span></span><br/>

<a NAME="E2:3"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_4.html#T56" title="WAYBEL_4:th.56">WAYBEL_4:56</a></span>;<br/>
<a NAME="E3:3"/><span class="kw">then </span>
not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E4:3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E4">A2</font></span>: 
not <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T18" title="WAYBEL_0:th.18">WAYBEL_0:18</a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:3"/>
<span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span>
  <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> or <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:3_1"/><span class="lab"><font color="Green" title="E5">A3</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">a1</font> = <font color="Maroon" title="c4">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E3:3_1"/>
not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E4:3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A4</font></span>: 
<font color="Maroon" title="c5">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E5:3_1"/><span class="lab"><font color="Green" title="E7">A5</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1"><span class="lab"><font color="Green" title="E5">A3</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E6:3_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T18" title="WAYBEL_0:th.18">WAYBEL_0:18</a></span>;<br/>
<a NAME="E7:3_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">x</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c5">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3_1"><span class="lab"><font color="Green" title="E6">A4</font></span></a>, <a class="ref" href="orders_2.html#D10" title="ORDERS_2:def.10">ORDERS_2:def 10</a></span>;<br/>
<a NAME="E8:3_1"/><span class="kw">then </span>
not <font color="Maroon" title="c5">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="waybel_4.html#T56" title="WAYBEL_4:th.56">WAYBEL_4:56</a></span>;<br/>
<a NAME="E9:3_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:3_1"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:3_1"><span class="lab"><font color="Green" title="E7">A5</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c4">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span> or <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E6:3"/><span class="lab"><font color="Green" title="E5">A6</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span><br/>

<a NAME="E7:3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A7</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">a1</font> = <font color="Maroon" title="c4">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:3"><span class="lab"><font color="Green" title="E5">A6</font></span></a></span>;<br/>
<a NAME="E9:3"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c3">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:3"><span class="lab"><font color="Green" title="E5">A6</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E10:3"/><span class="kw">then </span>
<font color="Maroon" title="c3">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c5">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T18" title="WAYBEL_0:th.18">WAYBEL_0:18</a></span>;<br/>
<a NAME="E11:3"/><span class="kw">then </span>
not <font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3"><span class="lab"><font color="Green" title="E4">A2</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:3"/>
<font color="Maroon" title="c4">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K6" title="WAYBEL_0:func.6">uparrow</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:3"><span class="lab"><font color="Green" title="E6">A7</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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