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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">  for <font color="Olive" title="b1">Si</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">XSeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Olive" title="b1">Si</font> holds   <a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Olive" title="b2">XSeq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Si</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Si</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</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">  for <font color="Olive" title="b1">XSeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Si</font> holds   <a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Olive" title="b1">XSeq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Si</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">XSeq</font> be   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Si</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="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Maroon" title="c3">XSeq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Si</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">x</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Maroon" title="c3">XSeq</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:3"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure1.html#K4" title="MEASURE1:func.4">rng</a> <font color="Maroon" title="c3">XSeq</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"> <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</font></span><br/>

<a NAME="E2:3"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">XSeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Olive" title="b1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="setlim_1.html#T4" onmouseover="rs('setlim_1/T4')" onmouseout="rh()">SETLIM_1:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:3"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Si</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"> verum</span><br/>


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