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

<b>let </b><font color="Maroon" title="c3">R1</font>, <font color="Maroon" title="c4">R2</font> be   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a> &amp; <font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a> &amp; <font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a> )</span><br/>



<a NAME="E1:12"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c3">R1</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <font color="Maroon" title="c4">R2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> )
 
<b>by </b><i><a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">h</font> be  <a href="fdiff_1.html#V1" title="FDIFF_1:attr.1">convergent_to_0</a> <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/><a NAME="E1:12_1"/><i><font color="Green" title="E9">A3</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>;<br/><a NAME="E2:12_1"/><i><font color="Green" title="E10">A4</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>;<br/><i><font color="Green" title="E11">A5</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="rfunct_2.html#T32" title="RFUNCT_2:th.32">RFUNCT_2:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T24" title="SEQ_1:th.24">SEQ_1:24</a></i>
;<br/><b>hence </b><a NAME="E4:12_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>by </b><i><a class="txt" href="#E1:12_1"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="#E2:12_1"><i><font color="Green" title="E10">A4</font></i></a>, <a class="ref" href="seq_2.html#T19" title="SEQ_2:th.19">SEQ_2:19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><b>thus </b> <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E1:12_1"><i><font color="Green" title="E9">A3</font></i></a>, <a class="txt" href="#E2:12_1"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="#E3:12_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="ref" href="seq_2.html#T20" title="SEQ_2:th.20">SEQ_2:20</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:12"/>
<font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a> &amp; <font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">h</font> be  <a href="fdiff_1.html#V1" title="FDIFF_1:attr.1">convergent_to_0</a> <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/><a NAME="E1:12_2"/><i><font color="Green" title="E9">A7</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>;<br/><a NAME="E2:12_2"/><i><font color="Green" title="E10">A8</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>;<br/><i><font color="Green" title="E11">A9</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="rfunct_2.html#T32" title="RFUNCT_2:th.32">RFUNCT_2:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T29" title="SEQ_1:th.29">SEQ_1:29</a></i>
;<br/><b>hence </b><a NAME="E4:12_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>by </b><i><a class="txt" href="#E1:12_2"><i><font color="Green" title="E9">A7</font></i></a>, <a class="txt" href="#E2:12_2"><i><font color="Green" title="E10">A8</font></i></a>, <a class="ref" href="seq_2.html#T25" title="SEQ_2:th.25">SEQ_2:25</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><b>thus </b> <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E1:12_2"><i><font color="Green" title="E9">A7</font></i></a>, <a class="txt" href="#E2:12_2"><i><font color="Green" title="E10">A8</font></i></a>, <a class="txt" href="#E3:12_2"><i><font color="Green" title="E11">A9</font></i></a>, <a class="ref" href="seq_2.html#T26" title="SEQ_2:th.26">SEQ_2:26</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:12"/>
<font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">h</font> be  <a href="fdiff_1.html#V1" title="FDIFF_1:attr.1">convergent_to_0</a> <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/><a NAME="E1:12_3"/><i><font color="Green" title="E9">A11</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>;<br/><a NAME="E2:12_3"/><i><font color="Green" title="E10">A12</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>;<br/><a NAME="E3:12_3"/><i><font color="Green" title="E11">A13</font></i>: 
( <font color="Maroon" title="c5">h</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a> &amp; <font color="Maroon" title="c5">h</font> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <font color="Maroon" title="c5">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="fdiff_1.html#D1" target="_self" title="FDIFF_1:def.1">Def1</a></i>;<br/><a NAME="E4:12_3"/><b>then </b><i><font color="Green" title="E12">A14</font></i>: 
<font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a>  is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-zero</a>
 <b>by </b><i><a class="ref" href="seq_1.html#T41" title="SEQ_1:th.41">SEQ_1:41</a></i>;<br/><a NAME="E5:12_3"/><i><font color="Green" title="E13">A15</font></i>: 
<font color="Maroon" title="c5">h</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>by </b><i><a class="txt" href="#E1:12_3"><i><font color="Green" title="E9">A11</font></i></a>, <a class="txt" href="#E3:12_3"><i><font color="Green" title="E11">A13</font></i></a>, <a class="ref" href="seq_2.html#T28" title="SEQ_2:th.28">SEQ_2:28</a></i>;<br/><i><font color="Green" title="E14">A16</font></i>:  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span></span>)</span> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E1:12_3"><i><font color="Green" title="E9">A11</font></i></a>, <a class="txt" href="#E3:12_3"><i><font color="Green" title="E11">A13</font></i></a>, <a class="ref" href="seq_2.html#T29" title="SEQ_2:th.29">SEQ_2:29</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/><i><font color="Green" title="E15">A17</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <font color="Maroon" title="c5">h</font>
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="rfunct_2.html#T32" title="RFUNCT_2:th.32">RFUNCT_2:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span></span>)</span> <a href="valued_1.html#K52" title="VALUED_1:func.52">/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:12_3"><i><font color="Green" title="E12">A14</font></i></a>, <a class="ref" href="seq_1.html#T51" title="SEQ_1:th.51">SEQ_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T44" title="SEQ_1:th.44">SEQ_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T22" title="SEQ_1:th.22">SEQ_1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T22" title="SEQ_1:th.22">SEQ_1:22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">R2</font> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#T22" title="SEQ_1:th.22">SEQ_1:22</a></i>
;<br/><b>hence </b><a NAME="E8:12_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>
 <b>by </b><i><a class="txt" href="#E2:12_3"><i><font color="Green" title="E10">A12</font></i></a>, <a class="txt" href="#E5:12_3"><i><font color="Green" title="E13">A15</font></i></a>, <a class="ref" href="seq_2.html#T28" title="SEQ_2:th.28">SEQ_2:28</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><b>thus </b> <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="valued_1.html#K37" title="VALUED_1:func.37">"</a> </span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font></span>)</span> <a href="funct_2.html#K8" title="FUNCT_2:func.8">/*</a> <font color="Maroon" title="c5">h</font></span>)</span></span>)</span> = 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="txt" href="#E2:12_3"><i><font color="Green" title="E10">A12</font></i></a>, <a class="txt" href="#E5:12_3"><i><font color="Green" title="E13">A15</font></i></a>, <a class="txt" href="#E6:12_3"><i><font color="Green" title="E14">A16</font></i></a>, <a class="txt" href="#E7:12_3"><i><font color="Green" title="E15">A17</font></i></a>, <a class="ref" href="seq_2.html#T29" title="SEQ_2:th.29">SEQ_2:29</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:12"/>
<font color="Maroon" title="c3">R1</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Maroon" title="c4">R2</font> is   <a href="fdiff_1.html#NM1" title="FDIFF_1:NM.1">REST</a>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="fdiff_1.html#D3" target="_self" title="FDIFF_1:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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