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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E1:74"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4 <a href="hidden.html#R1">=</a> 2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
;<br/>
<a NAME="E2:74"/><b>then </b><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4 <a href="hidden.html#R2">in</a>  <a href="fib_num2.html#K3" target="_self">EvenNAT</a> 
 
;<br/>
<a NAME="E3:74"/>
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<a NAME="E4:74"/><b>then </b>
not <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3 <a href="hidden.html#R2">in</a>  <a href="fib_num2.html#K3" target="_self">EvenNAT</a> 
 
<b>by </b><i><a class="ref" href="fib_num2.html#T53" target="_self">Th53</a></i>;<br/>
<a NAME="E5:74"/><b>then </b><i><font color="Green">E55</font></i>: 
<span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span><a href="seq_4.html#K1">}</a></span> <a href="xboole_0.html#R1">misses</a>  <a href="fib_num2.html#K3" target="_self">EvenNAT</a> 
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/>
<a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span> = 
<a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>

<br/>.= 
<a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="seq_4.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span><a href="seq_4.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T11">FINSEQ_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p2"><a href="seq_4.html#K1">{</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span><a href="seq_4.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span><a href="seq_4.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="fib_num2.html#E2:74"><i><font color="Green">E54</font></i></a>, <a class="ref" href="zfmisc_1.html#T52">ZFMISC_1:52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3"><a href="seq_4.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span><a href="seq_4.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span><a href="seq_4.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T11">FINSEQ_1:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p3"><a href="seq_4.html#K1">{</a><span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3</span>)</span></span><a href="seq_4.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span><a href="seq_4.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span><a href="seq_4.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="fib_num2.html#E5:74"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span><a href="seq_4.html#K1">}</a></span>

;<br/>
<b>hence </b><a NAME="E7:74"/>
<span class="p1">(<span class="default"><a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <a href="fib_num2.html#K3" target="_self">EvenNAT</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 4</span>)</span></span>)</span>
 ;<br/>


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