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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">X</font> being    <a href="mmlquery.html#L1" title="MMLQUERY:struct.1">ConstructorDB</a> <br/>  for <font color="Olive" title="b2">A</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="mmlquery.html#U1" title="MMLQUERY:sel.1">Constrs</a> of <font color="Olive" title="b1">X</font> holds   <a href="mmlquery.html#K32" title="MMLQUERY:func.32">ATLEAST</a> <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="mmlquery.html#K35" title="MMLQUERY:func.35">ATLEAST-</a> (<font color="Olive" title="b2">A</font>,<font color="Maroon" title="c1">n</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be    <a href="mmlquery.html#L1" title="MMLQUERY:struct.1">ConstructorDB</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">A</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="mmlquery.html#U1" title="MMLQUERY:sel.1">Constrs</a> of <font color="Maroon" title="c2">X</font> holds   <a href="mmlquery.html#K32" title="MMLQUERY:func.32">ATLEAST</a> <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="mmlquery.html#K35" title="MMLQUERY:func.35">ATLEAST-</a> (<font color="Olive" title="b1">A</font>,<font color="Maroon" title="c1">n</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="mmlquery.html#U1" title="MMLQUERY:sel.1">Constrs</a> of <font color="Maroon" title="c2">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">  <a href="mmlquery.html#K32" title="MMLQUERY:func.32">ATLEAST</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="mmlquery.html#K35" title="MMLQUERY:func.35">ATLEAST-</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>)</span><br/>





<a NAME="E1:99"/>
(  <a href="mmlquery.html#K32" title="MMLQUERY:func.32">ATLEAST</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mmlquery.html#K35" title="MMLQUERY:func.35">ATLEAST-</a> (<font color="Maroon" title="c3">A</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mmlquery.html#T67" target="_self" onmouseover="rs('mmlquery/T67')" onmouseout="rh()">Th67</a>, <a class="ref" href="nat_1.html#T2" onmouseover="rs('nat_1/T2')" onmouseout="rh()">NAT_1:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:99"/>
 <a href="mmlquery.html#K32" title="MMLQUERY:func.32">ATLEAST</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="mmlquery.html#K35" title="MMLQUERY:func.35">ATLEAST-</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c1">n</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mmlquery.html#T70" target="_self" onmouseover="rs('mmlquery/T70')" onmouseout="rh()">Th70</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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