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<span class="kw">let </span><font color="Maroon" title="c1">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">  for <font color="Olive" title="b1">i</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b2">p</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>  st <font color="Olive" title="b2">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b1">i</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b2">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Olive" title="b1">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">i</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">  for <font color="Olive" title="b1">p</font> being   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a>  st <font color="Olive" title="b1">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">i</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b1">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">i</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">p</font> be   <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</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="c3">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">i</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">n</font> implies <font color="Maroon" title="c3">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">i</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:7"/>
<font color="Maroon" title="c3">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">i</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">n</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">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">i</font></span><br/>

<a NAME="E2:7"/><span class="kw">then </span>
<font color="Maroon" title="c3">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">i</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">n</font></span>)</span></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="number14.html#T4" target="_self" onmouseover="rs('number14/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E3:7"/><span class="kw">then </span>
<font color="Maroon" title="c3">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><font color="Maroon" title="c2">i</font></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="taylor_2.html#T1" onmouseover="rs('taylor_2/T1')" onmouseout="rh()">TAYLOR_2:1</a></span>;<br/>
<a NAME="E4:7"/><span class="kw">then </span>
<font color="Maroon" title="c3">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default"><font color="Maroon" title="c2">i</font></span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_3.html#T5" onmouseover="rs('nat_3/T5')" onmouseout="rh()">NAT_3:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:7"/>
<font color="Maroon" title="c3">p</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c2">i</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="number14.html#T4" target="_self" onmouseover="rs('number14/T4')" onmouseout="rh()">Th4</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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