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<span class="kw">let </span><font color="Maroon" title="c1">n</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">  <a href="number14.html#K6" title="NUMBER14:func.6">PrimeDivisorsFS</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq2.html#K6" title="RFINSEQ2:func.6">sort_a</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p3">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">X</font> =  <a href="number12.html#K2" title="NUMBER12:func.2">PrimeDivisors</a> <font color="Maroon" title="c1">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">P</font> =  <a href="number14.html#K6" title="NUMBER14:func.6">PrimeDivisorsFS</a> <font color="Maroon" title="c1">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">f</font> =  <a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p2">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">S</font> =  <a href="rfinseq2.html#K6" title="RFINSEQ2:func.6">sort_a</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p3">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span>;<br/>
<a NAME="E1:75"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
 <a href="number14.html#K6" title="NUMBER14:func.6">PrimeDivisorsFS</a> <font color="Maroon" title="c1">n</font> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T106" onmouseover="rs('finseq_1/T106')" onmouseout="rh()">FINSEQ_1:106</a></span>;<br/>
<a NAME="E2:75"/>
 <a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p1">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p2">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T106" onmouseover="rs('finseq_1/T106')" onmouseout="rh()">FINSEQ_1:106</a></span>;<br/>
<a NAME="E3:75"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A2</font></span>: 
 <a href="rfinseq2.html#K6" title="RFINSEQ2:func.6">sort_a</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p3">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid_7.html#T13" onmouseover="rs('euclid_7/T13')" onmouseout="rh()">EUCLID_7:13</a></span>;<br/>
<a NAME="E4:75"/><span class="lab"><font color="Green" title="E56">A3</font></span>: 
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="number14.html#K6" title="NUMBER14:func.6">PrimeDivisorsFS</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="number12.html#K2" title="NUMBER12:func.2">PrimeDivisors</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D14" onmouseover="rs('finseq_1/D14')" onmouseout="rh()">FINSEQ_1:def 14</a></span>;<br/>
<a NAME="E5:75"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p3">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></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="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D3" onmouseover="rs('funct_2/D3')" onmouseout="rh()">FUNCT_2:def 3</a></span>;<br/>
<a NAME="E6:75"/><span class="kw">then </span>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="rfinseq2.html#K6" title="RFINSEQ2:func.6">sort_a</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p3">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p4">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span></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="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="classes1.html#T75" onmouseover="rs('classes1/T75')" onmouseout="rh()">CLASSES1:75</a>, <a class="ref" href="rfinseq2.html#D6" onmouseover="rs('rfinseq2/D6')" onmouseout="rh()">RFINSEQ2:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:75"/>
 <a href="number14.html#K6" title="NUMBER14:func.6">PrimeDivisorsFS</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq2.html#K6" title="RFINSEQ2:func.6">sort_a</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K20" title="FINSEQ_1:func.20">canFS</a> <span class="p2">(<span class="default"><a href="pre_poly.html#K22" title="PRE_POLY:func.22">support</a> <span class="p3">(<span class="default"><a href="nat_3.html#NK13" title="NAT_3:NK.13">pfexp</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:75"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E3:75"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="txt" href="#E4:75"><span class="lab"><font color="Green" title="E56">A3</font></span></a>, <a class="ref" href="number14.html#T48" target="_self" onmouseover="rs('number14/T48')" onmouseout="rh()">Th48</a>, <a class="ref" href="integra3.html#T6" onmouseover="rs('integra3/T6')" onmouseout="rh()">INTEGRA3:6</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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