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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <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="classes3.html#K1" title="CLASSES3:func.1">GrothendieckUniverse</a> <font color="Maroon" title="c1">X</font> is   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a> &amp; (  for <font color="Olive" title="b1">U</font> being   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>  st <font color="Maroon" title="c1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">U</font> holds <br/> <a href="classes3.html#K1" title="CLASSES3:func.1">GrothendieckUniverse</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">U</font> ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">G</font> =  <a href="classes3.html#K1" title="CLASSES3:func.1">GrothendieckUniverse</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">thus </span><a NAME="E1:34"/>
 <a href="classes3.html#K1" title="CLASSES3:func.1">GrothendieckUniverse</a> <font color="Maroon" title="c1">X</font> is   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="classes3.html#D4" target="_self" onmouseover="rs('classes3/D4')" onmouseout="rh()">Def4</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">  for <font color="Olive" title="b1">U</font> being   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>  st <font color="Maroon" title="c1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">U</font> holds <br/> <a href="classes3.html#K1" title="CLASSES3:func.1">GrothendieckUniverse</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">U</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">U</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</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"> ( <font color="Maroon" title="c1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font> implies  <a href="classes3.html#K1" title="CLASSES3:func.1">GrothendieckUniverse</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">U</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:34"/>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">U</font>
 ; <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="classes3.html#K1" title="CLASSES3:func.1">GrothendieckUniverse</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">U</font></span><br/>

<a NAME="E3:34"/><span class="kw">then </span>
<font color="Maroon" title="c3">U</font> is    <a href="classes3.html#M1" title="CLASSES3:mode.1">Grothendieck</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes3.html#D4" target="_self" onmouseover="rs('classes3/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:34"/>
 <a href="classes3.html#K1" title="CLASSES3:func.1">GrothendieckUniverse</a> <font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">U</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="classes3.html#D5" target="_self" onmouseover="rs('classes3/D5')" onmouseout="rh()">GDef</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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