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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  implies <font color="Maroon" title="c1">x</font> is  <a href="counters.html#V1" title="COUNTERS:attr.1">ext-natural</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:5_3_1"/>
<font color="Maroon" title="c1">x</font> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</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> is  <a href="counters.html#V1" title="COUNTERS:attr.1">ext-natural</a> </span><br/>

<a NAME="E2:5_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" onmouseover="rs('ordinal1/D12')" onmouseout="rh()">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:5_3_1"/>
<font color="Maroon" title="c1">x</font> is  <a href="counters.html#V1" title="COUNTERS:attr.1">ext-natural</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="counters.html#T1" target="_self" onmouseover="rs('counters/T1')" onmouseout="rh()">Th1</a>, <a class="ref" href="xboole_0.html#D8" onmouseover="rs('xboole_0/D8')" onmouseout="rh()">XBOOLE_0:def 8</a>, <a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI: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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