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<span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</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="c2">R</font> is  <a href="valued_2.html#V12" title="VALUED_2:attr.12">natural-functions-valued</a>  implies <font color="Maroon" title="c2">R</font> is  <a href="valued_2.html#V11" title="VALUED_2:attr.11">integer-functions-valued</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:67_1_1"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
 <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c2">R</font> is  <a href="valued_2.html#V6" title="VALUED_2:attr.6">natural-functions-membered</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="valued_2.html#D25" target="_self" title="VALUED_2:def.25">VALUED_2:def 25</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="c2">R</font> is  <a href="valued_2.html#V11" title="VALUED_2:attr.11">integer-functions-valued</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="valued_2.html#D6" target="_self" title="VALUED_2:def.6">VALUED_2:def 6</a>,<a class="ref" href="valued_2.html#D24" target="_self" title="VALUED_2:def.24">VALUED_2:def 24</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="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c2">R</font> implies <font color="Maroon" title="c3">y</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/>

<span class="kw">thus </span><a NAME="E2:67_1_1"/>
( <font color="Maroon" title="c3">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c2">R</font> implies <font color="Maroon" title="c3">y</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67_1_1"><span class="lab"><font color="Green" title="E32">A1</font></span></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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