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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>;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/>





<b>thus </b><a NAME="E1:168"/>
( <font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a> implies <font color="Maroon" title="c1">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> is <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="168_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon" title="c4">H1</font> being   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><b> such that </b><a NAME="E1:168_1"/><i><font color="Green" title="E70">A1</font></i>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c4">H1</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_lang.html#D12" title="ZF_LANG:def.12">ZF_LANG:def 12</a><br/>

<a NAME="E2:168_1"/>
<font color="Maroon" title="c1">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H1</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span>
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:168_1"><i><font color="Green" title="E70">A1</font></i></a>, <a class="ref" href="zf_lang1.html#T170" target="_self" title="ZF_LANG1:th.170">Th170</a></i>;<br/>
<b>hence </b><a NAME="E3:168_1"/>
<font color="Maroon" title="c1">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> is <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>
 <b>by </b><i><a class="ref" href="zf_lang.html#T16" title="ZF_LANG:th.16">ZF_LANG:16</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:168"/><i><font color="Green" title="E70">A2</font></i>: 
<font color="Maroon" title="c1">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> is <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>
 ;<br/>

<a NAME="E3:168"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3 &amp; 3 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T29" title="ZF_LANG:th.29">ZF_LANG:29</a></i>;<br/>
<a NAME="E4:168"/><b>then </b>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">H</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E5:168"/><b>then </b><i><font color="Green" title="E71">A3</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c1">H</font> )
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E2:168"><i><font color="Green" title="E70">A2</font></i></a>, <a class="ref" href="zf_lang1.html#T148" target="_self" title="ZF_LANG1:th.148">Th148</a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a>, <a class="ref" href="zf_lang.html#T37" title="ZF_LANG:th.37">ZF_LANG:37</a></i>;<br/>
<a NAME="E6:168"/><b>then </b>
<font color="Maroon" title="c1">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="ref" href="zf_lang1.html#D4" target="_self" title="ZF_LANG1:def.4">Def4</a></i>;<br/>
<a NAME="E7:168"/><b>then </b>
2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E5:168"><i><font color="Green" title="E71">A3</font></i></a>, <a class="ref" href="zf_lang1.html#D4" target="_self" title="ZF_LANG1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E8:168"/>
<font color="Maroon" title="c1">H</font> is <a href="zf_lang.html#V4" title="ZF_LANG:attr.4">negative</a>
 <b>by </b><i><a class="ref" href="zf_lang.html#T43" title="ZF_LANG:th.43">ZF_LANG:43</a></i>;<br/>


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