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<span class="kw">let </span><font color="Maroon" title="c2">it1</font>, <font color="Maroon" title="c3">it2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">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"> ( <font color="Maroon" title="c2">it1</font> <a href="jordan1h.html#R1" title="JORDAN1H:pred.1">is_sufficiently_large_for</a> <font color="Maroon" title="c1">C</font> &amp; (  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="jordan1h.html#R1" title="JORDAN1H:pred.1">is_sufficiently_large_for</a> <font color="Maroon" title="c1">C</font> holds <br/><font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">it1</font> ) &amp; <font color="Maroon" title="c3">it2</font> <a href="jordan1h.html#R1" title="JORDAN1H:pred.1">is_sufficiently_large_for</a> <font color="Maroon" title="c1">C</font> &amp; (  for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="jordan1h.html#R1" title="JORDAN1H:pred.1">is_sufficiently_large_for</a> <font color="Maroon" title="c1">C</font> holds <br/><font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">it2</font> ) implies <font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:3_1_2"/><span class="lab"><font color="Green" title="E3">A5</font></span>: 
<font color="Maroon" title="c2">it1</font> <a href="jordan1h.html#R1" title="JORDAN1H:pred.1">is_sufficiently_large_for</a> <font color="Maroon" title="c1">C</font>
 <span class="kw">and </span><br/><a NAME="E2:3_1_2"/><span class="lab"><font color="Green" title="E4">A6</font></span>: 
 for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="jordan1h.html#R1" title="JORDAN1H:pred.1">is_sufficiently_large_for</a> <font color="Maroon" title="c1">C</font> holds <br/><font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">it1</font>
 <span class="kw">and </span><br/><a NAME="E3:3_1_2"/><span class="lab"><font color="Green" title="E5">A7</font></span>: 
<font color="Maroon" title="c3">it2</font> <a href="jordan1h.html#R1" title="JORDAN1H:pred.1">is_sufficiently_large_for</a> <font color="Maroon" title="c1">C</font>
 <span class="kw">and </span><br/><a NAME="E4:3_1_2"/><span class="lab"><font color="Green" title="E6">A8</font></span>: 
 for <font color="Olive" title="b1">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">j</font> <a href="jordan1h.html#R1" title="JORDAN1H:pred.1">is_sufficiently_large_for</a> <font color="Maroon" title="c1">C</font> holds <br/><font color="Olive" title="b1">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">it2</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="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font></span><br/>

<a NAME="E5:3_1_2"/><span class="lab"><font color="Green" title="E7">A9</font></span>: 
<font color="Maroon" title="c3">it2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">it1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_2"><span class="lab"><font color="Green" title="E3">A5</font></span></a>, <a class="txt" href="#E4:3_1_2"><span class="lab"><font color="Green" title="E6">A8</font></span></a></span>;<br/>
<a NAME="E6:3_1_2"/>
<font color="Maroon" title="c2">it1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">it2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:3_1_2"><span class="lab"><font color="Green" title="E4">A6</font></span></a>, <a class="txt" href="#E3:3_1_2"><span class="lab"><font color="Green" title="E5">A7</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:3_1_2"/>
<font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:3_1_2"><span class="lab"><font color="Green" title="E7">A9</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</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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