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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:120_1_1_1"/>
( <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:120_1_1_1_1"/>
<a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font> st <font color="Olive">b<sub>1</sub></font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> </span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">e</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#D1" onmouseover="rs('subset_1/D1')" onmouseout="rh()">SUBSET_1:def 1</a></span>;<br/><span class="kw">take </span>
<font color="Maroon" title="c2">e</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">e</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> </span><br/><span class="kw">thus </span><a NAME="E3:120_1_1_1_1"/>
<font color="Maroon" title="c2">e</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:120_1_1_1_2"/>
<a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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">  ex <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font> st <font color="Olive">b<sub>1</sub></font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> </span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:120_1_1_1_2"/><span class="lab"><font color="Green" title="E80">A1</font></span>: 
<font color="Maroon" title="c2">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#T7" onmouseover="rs('xboole_0/T7')" onmouseout="rh()">XBOOLE_0:7</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c3">e</font> = <font color="Maroon" title="c2">e</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="fib_num2.html#K3" title="FIB_NUM2:func.3">EvenNAT</a> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:120_1_1_1_2"><span class="lab"><font color="Green" title="E80">A1</font></span></a></span>;<br/><span class="kw">take </span>
<font color="Maroon" title="c3">e</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="c3">e</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a> </span><br/><span class="kw">thus </span><a NAME="E5:120_1_1_1_2"/>
<font color="Maroon" title="c3">e</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</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"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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