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<b>set </b><font color="Maroon" title="c1">A</font> =  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> ;<br/>
<b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="aofa_i00.html#D23" target="_self" title="AOFA_I00:def.23">AOFA_I00:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">T</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span>  ex <font color="Olive" title="b2">f</font> being   <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> ,<font color="Olive" title="b1">T</font> st <font color="Olive" title="b2">f</font> is <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a></span><br/><b>let </b><font color="Maroon" title="c3">T</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> </span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being   <a href="aofa_000.html#M1" title="AOFA_000:mode.1">ExecutionFunction</a> of  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<a href="aofa_i00.html#K26" title="AOFA_I00:func.26">INT-ElemIns</a> , <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c2">X</font>,<a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> ,<font color="Maroon" title="c3">T</font> st <font color="Olive" title="b1">f</font> is <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a></span><br/>



<b>consider </b><font color="Maroon" title="c4">c</font> being   <a href="aofa_i00.html#NM2" title="AOFA_I00:NM.2">Enumeration</a> of <font color="Maroon" title="c2">X</font>;<br/>
<b>consider </b><font color="Maroon" title="c5">f</font> being    <a href="aofa_i00.html#M6" title="AOFA_I00:mode.6">INT-Exec</a> of <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">T</font>;<br/>
<b>take </b>
<font color="Maroon" title="c5">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">f</font> is <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a></span><br/>

<b>thus </b><a NAME="E3:53_1_1"/>
<font color="Maroon" title="c5">f</font> is <a href="aofa_i00.html#V1" title="AOFA_I00:attr.1">Euclidean</a>
 ; <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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