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<b>let </b><font color="Maroon" title="c1">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a> implies  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )</span><br/>

<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3</span><br/>

<div><i><font color="Green" title="E18">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:30_1"/>
<font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V2" title="ZF_LANG:attr.2">being_equality</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3</span><br/><b>then consider </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a><b> such that </b><br/><a NAME="E3:30_1"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D10" target="_self" title="ZF_LANG:def.10">Def10</a></i>;<br/><a NAME="E4:30_1"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="#E3:30_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="finseq_1.html#D10" title="FINSEQ_1:def.10">FINSEQ_1:def 10</a></i>;<br/><b>hence </b><a NAME="E5:30_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 <b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:30_2"/>
<font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V3" title="ZF_LANG:attr.3">being_membership</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3</span><br/><b>then consider </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a><b> such that </b><br/><a NAME="E3:30_2"/><i><font color="Green" title="E19">A4</font></i>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D11" target="_self" title="ZF_LANG:def.11">Def11</a></i>;<br/><a NAME="E4:30_2"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default">1,<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="#E3:30_2"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="finseq_1.html#D10" title="FINSEQ_1:def.10">FINSEQ_1:def 10</a></i>;<br/><b>hence </b><a NAME="E5:30_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 <b>by </b><i><a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:30"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 <b>by </b><i><a class="txt" href="#E1:30"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="#E2:30"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="zf_lang.html#D15" target="_self" title="ZF_LANG:def.15">Def15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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