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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">I</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c2">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E2:11"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" onmouseover="rs('xboole_0/D1')" onmouseout="rh()">XBOOLE_0:def 1</a></span>;<br/>
<span class="kw">thus </span><a NAME="E3:11"/>
 <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c1">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">I</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_9.html#T3" target="_self" onmouseover="rs('msualg_9/T3')" onmouseout="rh()">Th3</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">I</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">q</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">I</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> or <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c1">I</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E4:11"/>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">I</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c1">I</font></span>)</span></span><br/>

<a NAME="E5:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A2</font></span>: 
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" onmouseover="rs('tarski/D1')" onmouseout="rh()">TARSKI:def 1</a></span>;<br/>
<a NAME="E6:11"/>
 <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c1">I</font></span>)</span>,<font color="Maroon" title="c2">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="eqrel_1.html#T26" onmouseover="rs('eqrel_1/T26')" onmouseout="rh()">EQREL_1:26</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:11"/>
<font color="Maroon" title="c3">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K1" title="EQREL_1:func.1">nabla</a> <font color="Maroon" title="c1">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:11"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="ref" href="eqrel_1.html#D3" onmouseover="rs('eqrel_1/D3')" onmouseout="rh()">EQREL_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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