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<span class="kw">set </span><font color="Maroon" title="c2">A</font> =  the   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>;<br/>
<a NAME="E1:17_1_1"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
(  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a>  the   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_0.html#D3" onmouseover="rs('valued_0/D3')" onmouseout="rh()">VALUED_0:def 3</a>, <a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">A</font> =  the   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> as   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17_1_1"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="funct_2.html#T2" onmouseover="rs('funct_2/T2')" onmouseout="rh()">FUNCT_2:2</a></span>;<br/>
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<font color="Maroon" title="c3">A</font> is  <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E4:17_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="struct_0.html#NM5" title="STRUCT_0:NM.5">Function</a> of <font color="Maroon" title="c1">X</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> st <font color="Olive">b<sub>1</sub></font> is  <a href="valued_0.html#V6" title="VALUED_0:attr.6">natural-valued</a> 
 ; <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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