<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">A</font> be   <a href="aofa_i00.html#V2" title="AOFA_I00:attr.2">Euclidean</a>  <a href="aofa_000.html#NM1" title="AOFA_000:NM.1">preIfWhileAlgebra</a>; <a class="txt" 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   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/>  for <font color="Olive" title="b2">s</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b1">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)<br/>  for <font color="Olive" title="b3">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b4">g</font> being   <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>   <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b1">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>),<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b1">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b3">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)<br/>  for <font color="Olive" title="b5">t</font> being    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of <font color="Maroon" title="c1">A</font>,<font color="Olive" title="b4">g</font> holds <br/> ( (  not <font color="Olive" title="b5">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Olive" title="b4">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b1">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b3">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Olive" title="b4">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b1">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b3">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies  not <font color="Olive" title="b5">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) &amp; ( <font color="Olive" title="b5">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Olive" title="b4">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b1">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b3">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Olive" title="b4">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b2">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b5">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Olive" title="b1">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b3">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies <font color="Olive" title="b5">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)<br/>  for <font color="Olive" title="b2">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X</font><br/>  for <font color="Olive" title="b3">g</font> being   <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>   <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>),<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b2">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)<br/>  for <font color="Olive" title="b4">t</font> being    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of <font color="Maroon" title="c1">A</font>,<font color="Olive" title="b3">g</font> holds <br/> ( (  not <font color="Olive" title="b4">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Olive" title="b3">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b2">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Olive" title="b3">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b2">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies  not <font color="Olive" title="b4">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) &amp; ( <font color="Olive" title="b4">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Olive" title="b3">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b2">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Olive" title="b3">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b1">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b4">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b2">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies <font color="Olive" title="b4">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X</font><br/>  for <font color="Olive" title="b2">g</font> being   <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>   <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>),<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b1">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)<br/>  for <font color="Olive" title="b3">t</font> being    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of <font color="Maroon" title="c1">A</font>,<font color="Olive" title="b2">g</font> holds <br/> ( (  not <font color="Olive" title="b3">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Olive" title="b2">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b1">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Olive" title="b2">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b1">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies  not <font color="Olive" title="b3">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) &amp; ( <font color="Olive" title="b3">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Olive" title="b2">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b1">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Olive" title="b2">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b3">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Olive" title="b1">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies <font color="Olive" title="b3">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">g</font> being   <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>   <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>),<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)<br/>  for <font color="Olive" title="b2">t</font> being    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of <font color="Maroon" title="c1">A</font>,<font color="Olive" title="b1">g</font> holds <br/> ( (  not <font color="Olive" title="b2">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Olive" title="b1">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Olive" title="b1">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies  not <font color="Olive" title="b2">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) &amp; ( <font color="Olive" title="b2">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Olive" title="b1">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Olive" title="b1">g</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b2">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies <font color="Olive" title="b2">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">f</font> be   <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>   <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of <font color="Maroon" title="c1">A</font>, <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>),<span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t</font> being    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c5">f</font> holds <br/> ( (  not <font color="Olive" title="b1">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies  not <font color="Olive" title="b1">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) &amp; ( <font color="Olive" title="b1">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies <font color="Olive" title="b1">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">t</font> be    <a href="aofa_i00.html#M3" title="AOFA_I00:mode.3">INT-Expression</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c5">f</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  not <font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies  not <font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) &amp; ( <font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  implies <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) ) &amp; ( <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) implies <font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  ) )</span><br/>











<a NAME="E1:115"/><span class="lab"><font color="Green" title="E62">A1</font></span>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_ff.html#T6" title="PRE_FF:th.6">PRE_FF:6</a></span>;<br/>
<a NAME="E2:115"/><span class="lab"><font color="Green" title="E63">A2</font></span>: 
<font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T59" title="INT_1:th.59">INT_1:59</a></span>;<br/>
<a NAME="E3:115"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>)</span>)</span> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aofa_i00.html#T48" target="_self" title="AOFA_I00:th.48">Th48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:115"/>
(  not <font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  iff <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K65" title="AOFA_I00:func.65">is_odd</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:115"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E2:115"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="aofa_i00.html#T2" target="_self" title="AOFA_I00:th.2">Th2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  iff <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) )</span><br/>

<a NAME="E5:115"/><span class="lab"><font color="Green" title="E64">A3</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_ff.html#T6" title="PRE_FF:th.6">PRE_FF:6</a></span>;<br/>
<a NAME="E6:115"/><span class="lab"><font color="Green" title="E65">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">div</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T59" title="INT_1:th.59">INT_1:59</a></span>;<br/>
<a NAME="E7:115"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>)</span>)</span> <a href="aofa_i00.html#K21" title="AOFA_I00:func.21">.</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aofa_i00.html#T48" target="_self" title="AOFA_I00:th.48">Th48</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:115"/>
( <font color="Maroon" title="c6">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">s</font> is  <a href="abian.html#V1" title="ABIAN:attr.1">even</a>  iff <font color="Maroon" title="c5">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c3">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="aofa_i00.html#K66" title="AOFA_I00:func.66">is_even</a></span>)</span>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> (<font color="Maroon" title="c2">X</font>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>)</span>)</span> <a href="aofa_i00.html#K1" title="AOFA_I00:func.1">\</a> (<font color="Maroon" title="c4">b</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:115"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="txt" href="#E6:115"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="ref" href="aofa_i00.html#T2" target="_self" title="AOFA_I00:th.2">Th2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
