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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">T-Sequence</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">A</font> being  <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> holds  <font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Olive" title="b1">A</font></span>)</span> is   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">T-Sequence</a></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <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="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span> is   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">T-Sequence</a></span><br/>



<a NAME="E1:14"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <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="c3">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> implies ( <font color="Maroon" title="c3">X</font> is   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> ) )</span><br/><span class="kw">assume </span><a NAME="E1:14_1"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span></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="c3">X</font> is   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a> &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> )</span><br/><a NAME="E2:14_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A3</font></span>: 
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><span class="kw">hence </span><a NAME="E3:14_1"/>
<font color="Maroon" title="c3">X</font> is   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>
 ; <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="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span></span><br/><a NAME="E4:14_1"/>
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E8">A2</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="E5:14_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A4</font></span>: 
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D2" title="ORDINAL1:def.2">ORDINAL1:def 2</a></span>;<br/><a NAME="E6:14_1"/>
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="ref" href="ordinal1.html#D2" title="ORDINAL1:def.2">ORDINAL1:def 2</a></span>;<br/><span class="kw">hence </span><a NAME="E7:14_1"/>
<font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="txt" href="#E5:14_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</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>
<a NAME="E3:14"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span></span>)</span> is   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#T31" title="ORDINAL1:th.31">ORDINAL1:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14"/>
<font color="Maroon" title="c1">L</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c2">A</font></span>)</span> is   <a href="ordinal1.html#NM3" title="ORDINAL1:NM.3">T-Sequence</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#T46" title="ORDINAL1:th.46">ORDINAL1:46</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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