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<b>let </b><font color="Maroon" title="c1">E</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span><br/> for <font color="Olive" title="b2">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st  <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b2">n</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">E</font> <a href="catalan2.html#K3" title="CATALAN2:func.3">^omega</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st  <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Olive" title="b1">n</font></span><br/><b>let </b><font color="Maroon" title="c3">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font> )</span><br/>





<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E11">A1</font></i>: 
 <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_1"/>
( <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_1"><b>suppose </b></a><a NAME="E1:17_1_1"/><i><font color="Green" title="E12">A2</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span><br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  = 
<span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> 
<b>by </b><i><a class="ref" href="flang_1.html#T25" title="FLANG_1:th.25">FLANG_1:25</a></i>
<br/>.= 
<span class="p1"><a href="flang_1.html#K4" title="FLANG_1:func.4">{</a><span class="default"><span class="p2">(<span class="default"><a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c1">E</font></span>)</span></span><a href="flang_1.html#K4" title="FLANG_1:func.4">}</a></span>
<b>by </b><i><a class="ref" href="flang_1.html#T48" title="FLANG_1:th.48">FLANG_1:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font>
<b>by </b><i><a class="txt" href="#E1:17_1_1"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="flang_1.html#T25" title="FLANG_1:th.25">FLANG_1:25</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_1_2"><b>suppose </b></a><a NAME="E1:17_1_2"/><i><font color="Green" title="E12">A3</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span><br/><div class="add"><a NAME="E2:17_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> 
 <b>by </b><i><a class="ref" href="flang_1.html#T67" title="FLANG_1:th.67">FLANG_1:67</a></i>;<br/><b>hence </b><a NAME="E3:17_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font></span>)</span> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="flang_1.html#K8" title="FLANG_1:func.8">*</a> </span>)</span> <a href="flang_1.html#K7" title="FLANG_1:func.7">|^</a> <font color="Maroon" title="c3">n</font>
 <b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="#E1:17_1_2"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="flang_2.html#T16" target="_self" title="FLANG_2:th.16">Th16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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