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<b>let </b><font color="Maroon" title="c3">S</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">S</font> is <a href="valued_2.html#V5" title="VALUED_2:attr.5">integer-functions-membered</a></span><br/><b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="valued_2.html#D5" target="_self" title="VALUED_2:def.5">VALUED_2:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> implies <font color="Maroon" title="c4">x</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">integer-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> )</span><br/>



<b>thus </b><a NAME="E1:17_1_1"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> implies <font color="Maroon" title="c4">x</font> is  <a href="valued_0.html#V5" title="VALUED_0:attr.5">integer-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> )
 <b>by </b><i><a class="ref" href="valued_2.html#D5" target="_self" title="VALUED_2:def.5">Def5</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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