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<span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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"> ( <font color="Maroon" title="c2">f</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="asympt_3.html#K2" title="ASYMPT_3:func.2">R_Algebra_of_Big_Oh_poly</a>  iff <font color="Maroon" title="c2">f</font> is   <a href="asympt_3.html#V1" title="ASYMPT_3:attr.1">polynomially-abs-bounded</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> )</span><br/>

<a NAME="E1:25"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="asympt_3.html#K2" title="ASYMPT_3:func.2">R_Algebra_of_Big_Oh_poly</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="asympt_3.html#K1" title="ASYMPT_3:func.1">Big_Oh_poly</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="asympt_3.html#D3" target="_self" onmouseover="rs('asympt_3/D3')" onmouseout="rh()">defAlgebra</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:25"/>
( <font color="Maroon" title="c2">f</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="asympt_3.html#K2" title="ASYMPT_3:func.2">R_Algebra_of_Big_Oh_poly</a>  iff <font color="Maroon" title="c2">f</font> is   <a href="asympt_3.html#V1" title="ASYMPT_3:attr.1">polynomially-abs-bounded</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="asympt_3.html#D2" target="_self" onmouseover="rs('asympt_3/D2')" onmouseout="rh()">DefX1</a></span>; <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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