<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</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">  for <font color="Olive" title="b1">v</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="asympt_3.html#K2" title="ASYMPT_3:func.2">R_Algebra_of_Big_Oh_poly</a>  st <font color="Olive" title="b1">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_3.html#K3" title="ASYMPT_3:func.3">negligibleFuncs</a>  holds <br/><font color="Maroon" title="c2">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b1">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_3.html#K3" title="ASYMPT_3:func.3">negligibleFuncs</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">v</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <a href="asympt_3.html#K2" title="ASYMPT_3:func.2">R_Algebra_of_Big_Oh_poly</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="c3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_3.html#K3" title="ASYMPT_3:func.3">negligibleFuncs</a>  implies <font color="Maroon" title="c2">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_3.html#K3" title="ASYMPT_3:func.3">negligibleFuncs</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:51"/>
<font color="Maroon" title="c3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_3.html#K3" title="ASYMPT_3:func.3">negligibleFuncs</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">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_3.html#K3" title="ASYMPT_3:func.3">negligibleFuncs</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">v1</font> = <font color="Maroon" title="c3">v</font> as   <a href="asympt_3.html#V2" title="ASYMPT_3:attr.2">negligible</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#D5" target="_self" onmouseover="rs('asympt_3/D5')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E3:51"/>
<font color="Maroon" title="c2">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c4">v1</font> is  <a href="asympt_3.html#V2" title="ASYMPT_3:attr.2">negligible</a> 
 
;<br/>
<a NAME="E4:51"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">v</font> is   <a href="asympt_3.html#V2" title="ASYMPT_3:attr.2">negligible</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#T29" target="_self" onmouseover="rs('asympt_3/T29')" onmouseout="rh()">RSSPAC3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:51"/>
<font color="Maroon" title="c2">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Maroon" title="c3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="asympt_3.html#K3" title="ASYMPT_3:func.3">negligibleFuncs</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="asympt_3.html#D5" target="_self" onmouseover="rs('asympt_3/D5')" onmouseout="rh()">Def1</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/>


</div>
