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<span class="kw">let </span><font color="Maroon" title="c1">h</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</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="c1">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">X</font> =  <a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">f</font> =  <a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p1">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span>;<br/>
<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E40">A1</font></span>: 
<font color="Maroon" title="c1">h</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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">  for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">n</font> be   <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="c4">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> implies <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:50"/>
<font color="Maroon" title="c4">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</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"> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> </span><br/>

<a NAME="E3:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A2</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<a NAME="E4:50"/>
 <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E40">A1</font></span></a>, <a class="ref" href="finseq_1.html#D14" onmouseover="rs('finseq_1/D14')" onmouseout="rh()">FINSEQ_1:def 14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:50"/>
<span class="p1">(<span class="default"><a href="finseq_1.html#K14" title="FINSEQ_1:func.14">Sgm</a> <span class="p2">(<span class="default"><a href="number14.html#K5" title="NUMBER14:func.5">PrimeDivisors&gt;3</a> <font color="Maroon" title="c1">h</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E41">A2</font></span></a>, <a class="ref" href="number14.html#T37" target="_self" onmouseover="rs('number14/T37')" onmouseout="rh()">Th37</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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