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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><br/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being  <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <font color="Olive">b<sub>1</sub></font> <a href="finseq_1.html#V3" title="FINSEQ_1:attr.3">-long</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds  <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Olive" title="b3">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Olive" title="b3">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Olive" title="b2">f1</font>,<font color="Olive" title="b3">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font> being  <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <font color="Maroon" title="c2">n</font> <a href="finseq_1.html#V3" title="FINSEQ_1:attr.3">-long</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> holds  <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Olive" title="b2">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Olive" title="b2">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">f2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <font color="Maroon" title="c2">n</font> <a href="finseq_1.html#V3" title="FINSEQ_1:attr.3">-long</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">F</font> =  <a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span>;<br/>
<span class="lab"><font color="Green" title="E5">A1</font></span>:  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> = 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D11" title="VALUED_1:def.11">VALUED_1:def 11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">f2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T12" title="VALUED_1:th.12">VALUED_1:12</a></span>
;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">m</font> =  <a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font>;<br/>
<a NAME="E2:17"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c2">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T3" title="EUCLID:th.3">EUCLID:3</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:17_2"/>
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font> or  not <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_2_1"><span class="kw">suppose </span></a><a NAME="E1:17_2_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span></span><br/><div class="add"><a NAME="E2:17_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E7">A3</font></span>: 
<span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></span>;<br/><a NAME="E3:17_2_1"/><span class="kw">then </span>
 <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p2">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_2.html#D6" title="XXREAL_2:def.6">XXREAL_2:def 6</a></span>;<br/><a NAME="E4:17_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p4">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T142" title="FUNCT_1:th.142">FUNCT_1:142</a></span>;<br/><a NAME="E5:17_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <span class="p3">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p4">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p5">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D13" title="FUNCT_1:def.13">FUNCT_1:def 13</a></span>;<br/><a NAME="E6:17_2_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <span class="p2">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:17_2_1"/>
<span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17_2_1"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="ref" href="xxreal_2.html#T4" title="XXREAL_2:th.4">XXREAL_2:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_2_2"><span class="kw">suppose </span></a><a NAME="E1:17_2_2"/>
not <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c3">f1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span></span><br/><div class="add"><a NAME="E2:17_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E7">A4</font></span>: 
not <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><a NAME="E3:17_2_2"/>
<span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#T18" title="VALUED_1:th.18">VALUED_1:18</a></span>;<br/><span class="kw">hence </span><a NAME="E4:17_2_2"/>
<span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="euclid.html#K3" title="EUCLID:func.3">abs</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="rvsum_1.html#K8" title="RVSUM_1:func.8">-</a> <font color="Maroon" title="c4">f2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="euclid_9.html#K1" title="EUCLID_9:func.1">max_diff_index</a> <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c4">f2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17_2_2"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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