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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V3" title="ZF_LANG:attr.3">being_membership</a>  implies <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var1</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K19" title="ZF_LANG:func.19">Var2</a> <font color="Maroon" title="c1">H</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:68"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var1</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K19" title="ZF_LANG:func.19">Var2</a> <font color="Maroon" title="c1">H</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:68"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#D11" target="_self" title="ZF_LANG:def.11">Def11</a></span>;<br/>
<a NAME="E4:68"/>
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2"><a href="zf_lang.html#K3" title="ZF_LANG:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font></span><a href="zf_lang.html#K3" title="ZF_LANG:func.3">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="zf_lang.html#K3" title="ZF_LANG:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">y</font></span><a href="zf_lang.html#K3" title="ZF_LANG:func.3">*&gt;</a></span> <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D10" title="FINSEQ_1:def.10">FINSEQ_1:def 10</a></span>;<br/>
<a NAME="E5:68"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A3</font></span>: 
( <font color="Maroon" title="c1">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c1">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="finseq_1.html#T62" title="FINSEQ_1:th.62">FINSEQ_1:62</a></span>;<br/>
<a NAME="E6:68"/><span class="lab"><font color="Green" title="E41">A4</font></span>: 
<font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V7" title="ZF_LANG:attr.7">atomic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="zf_lang.html#D15" target="_self" title="ZF_LANG:def.15">Def15</a></span>;<br/>
<a NAME="E7:68"/><span class="kw">then </span>
<font color="Maroon" title="c1">H</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var1</a> <font color="Maroon" title="c1">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#D28" target="_self" title="ZF_LANG:def.28">Def28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:68"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K18" title="ZF_LANG:func.18">Var1</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K19" title="ZF_LANG:func.19">Var2</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="txt" href="#E6:68"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="#E5:68"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="zf_lang.html#D29" target="_self" title="ZF_LANG:def.29">Def29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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