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<b>let </b><font color="Maroon">H</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_1"/>
not <font color="Maroon">H</font> is <a href="zf_lang.html#V7" target="_self">atomic</a>
 ;<br/><b>then consider </b><font color="Maroon">H1</font> being   <a href="zf_lang.html#NM2">ZF-formula</a><b> such that </b><br/><a NAME="E3:33_1"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i/>;<br/><div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_1_1"/>
<font color="Maroon">H1</font> is <a href="zf_lang.html#V7" target="_self">atomic</a>
 ;<br/><a NAME="E2:33_1_1"/><b>then </b>
( 3 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp; 3 <a href="xxreal_0.html#R1">&lt;=</a> 3 <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:33_1_1"/>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_1_2"/>
not <font color="Maroon">H1</font> is <a href="zf_lang.html#V7" target="_self">atomic</a>
 ;<br/><b>then consider </b><font color="Maroon">F</font> being   <a href="zf_lang.html#NM2">ZF-formula</a><b> such that </b><br/><a NAME="E3:33_1_2"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font>
 <b>by </b><i/>;<br/><a NAME="E4:33_1_2"/><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><div><i><font color="Green">E40</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_1_2_1"/>
<font color="Maroon">F</font> is <a href="zf_lang.html#V7" target="_self">atomic</a>
 ;<br/><a NAME="E2:33_1_2_1"/><b>then </b>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> 3
 <b>by </b><i/>;<br/><a NAME="E3:33_1_2_1"/><b>then </b>
( <span class="p1">(<span class="default">3 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font> &amp; 3 <a href="xxreal_0.html#R1">&lt;=</a> 5 )
 <b>by </b><i>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E4:33_1_2_1"/>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:33_1_2_2"/>
not <font color="Maroon">F</font> is <a href="zf_lang.html#V7" target="_self">atomic</a>
 ;<br/><b>then consider </b><font color="Maroon">F1</font> being   <a href="zf_lang.html#NM2">ZF-formula</a><b> such that </b><br/><a NAME="E3:33_1_2_2"/><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 <b>by </b><i/>;<br/><a NAME="E4:33_1_2_2"/>
0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/><a NAME="E5:33_1_2_2"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E6:33_1_2_2"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E7:33_1_2_2"/><b>then </b>
1 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E8:33_1_2_2"/><b>then </b>
2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E9:33_1_2_2"/><b>then </b>
2 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">H1</font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><b>hence </b><a NAME="E10:33_1_2_2"/>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:33_1_2"/>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:33_1"/>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:33"/>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">H</font>
 <b>by </b><i/>;<br/>


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