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<span class="kw">let </span><font color="Maroon" title="c2">v</font>, <font color="Maroon" title="c3">u</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="c2">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>  &amp; <font color="Maroon" title="c3">u</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">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">u</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="E1:52"/>
( <font color="Maroon" title="c2">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>  &amp; <font color="Maroon" title="c3">u</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">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">u</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="c2">v</font>, <font color="Maroon" title="c5">u1</font> = <font color="Maroon" title="c3">u</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="E3:52"/>
<font color="Maroon" title="c4">v1</font> <a href="series_1.html#K1" title="SERIES_1:func.1">+</a> <font color="Maroon" title="c5">u1</font> is  <a href="asympt_3.html#V2" title="ASYMPT_3:attr.2">negligible</a> 
 
;<br/>
<a NAME="E4:52"/><span class="kw">then </span>
<font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">u</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#T27" target="_self" onmouseover="rs('asympt_3/T27')" onmouseout="rh()">RSSPAC2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:52"/>
<font color="Maroon" title="c2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">u</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/>


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