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( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V2" title="ZF_LANG:attr.2">being_equality</a>  or <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V3" title="ZF_LANG:attr.3">being_membership</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E24">A1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">k</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> , <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> being   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a><span class="kw"> such that </span><br/><a NAME="E3:47_1_1"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="trees_3.html#K14" title="TREES_3:func.14">&lt;*</a><span class="default"><font color="Maroon" title="c2">k</font></span><a href="trees_3.html#K14" title="TREES_3:func.14">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="trees_3.html#K14" title="TREES_3:func.14">&lt;*</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="trees_3.html#K14" title="TREES_3:func.14">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="trees_3.html#K14" title="TREES_3:func.14">&lt;*</a><span class="default"><font color="Maroon" title="c4">y</font></span><a href="trees_3.html#K14" title="TREES_3:func.14">*&gt;</a></span>
 ;<br/>
<a NAME="E4:47_1_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"><font color="Maroon" title="c2">k</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:47_1_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="ref" href="finseq_1.html#D10" onmouseover="rs('finseq_1/D10')" onmouseout="rh()">FINSEQ_1:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:47_1_1"/>
<font color="Maroon" title="c1">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 is   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T45" onmouseover="rs('finseq_1/T45')" onmouseout="rh()">FINSEQ_1:45</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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