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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:15_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">p</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><b>assume </b><a NAME="E2:15_1"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   holds <br/>(  not 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">n</font> or  not <font color="Olive">n</font> <a href="binop_2.html#K24">*</a> <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> or  not <font color="Olive">n</font> is <a href="int_2.html#V1">prime</a> or  not <font color="Olive">n</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">p</font> )
 ;<br/><a NAME="E3:15_1"/><b>then </b>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   holds <br/>(  not <font color="Olive">n</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">p</font> or  not 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">n</font> or  not <font color="Olive">n</font> <a href="binop_2.html#K24">*</a> <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> or  not <font color="Olive">n</font> is <a href="int_2.html#V1">prime</a> )
 ;<br/><b>hence </b><a NAME="E4:15_1"/>
<font color="Maroon">p</font> is <a href="int_2.html#V1">prime</a>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:15"/>
for <font color="Olive">p</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds <br/> ( <font color="Olive">p</font> is <a href="int_2.html#V1">prime</a> iff ( <font color="Olive">p</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st 1 <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">n</font> &amp; <font color="Olive">n</font> <a href="binop_2.html#K24">*</a> <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">p</font> &amp; <font color="Olive">n</font> is <a href="int_2.html#V1">prime</a> holds <br/> not <font color="Olive">n</font> <a href="nat_1.html#R1">divides</a> <font color="Olive">p</font> ) ) )
 <b>by </b><i/>;<br/>


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