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

<span class="kw">let </span><font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">t</font> be   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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">s</font>,<font color="Maroon" title="c3">t</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  implies  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="number08.html#K1" title="NUMBER08:func.1">Euler_factorization</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="number08.html#K1" title="NUMBER08:func.1">Euler_factorization</a> <font color="Maroon" title="c3">t</font></span>)</span> )</span><br/>

<a NAME="E1:35"/><span class="lab"><font color="Green" title="E36">A1</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="number08.html#K1" title="NUMBER08:func.1">Euler_factorization</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK15" title="NAT_3:NK.15">ppf</a> <font color="Maroon" title="c2">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="number08.html#D1" target="_self" onmouseover="rs('number08/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E2:35"/><span class="lab"><font color="Green" title="E37">A2</font></span>: 
 <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="number08.html#K1" title="NUMBER08:func.1">Euler_factorization</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK15" title="NAT_3:NK.15">ppf</a> <font color="Maroon" title="c3">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="number08.html#D1" target="_self" onmouseover="rs('number08/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E3:35"/><span class="lab"><font color="Green" title="E38">A3</font></span>: 
 <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK15" title="NAT_3:NK.15">ppf</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c2">s</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_3.html#D9" onmouseover="rs('nat_3/D9')" onmouseout="rh()">NAT_3:def 9</a></span>;<br/>
<a NAME="E4:35"/>
 <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK15" title="NAT_3:NK.15">ppf</a> <font color="Maroon" title="c3">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p1">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c3">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_3.html#D9" onmouseover="rs('nat_3/D9')" onmouseout="rh()">NAT_3:def 9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:35"/>
( <font color="Maroon" title="c2">s</font>,<font color="Maroon" title="c3">t</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  implies  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="number08.html#K1" title="NUMBER08:func.1">Euler_factorization</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="number08.html#K1" title="NUMBER08:func.1">Euler_factorization</a> <font color="Maroon" title="c3">t</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:35"><span class="lab"><font color="Green" title="E36">A1</font></span></a>, <a class="txt" href="#E2:35"><span class="lab"><font color="Green" title="E37">A2</font></span></a>, <a class="txt" href="#E3:35"><span class="lab"><font color="Green" title="E38">A3</font></span></a>, <a class="ref" href="nat_3.html#T44" onmouseover="rs('nat_3/T44')" onmouseout="rh()">NAT_3:44</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/>


</div>
