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<span class="kw">let </span><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</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="c1">f</font>,<font color="Maroon" title="c2">g</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</a>  implies  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c2">g</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:18"/>
<font color="Maroon" title="c1">f</font>,<font color="Maroon" title="c2">g</font> <a href="classes1.html#R2" title="CLASSES1:pred.2">are_fiberwise_equipotent</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">  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c2">g</font></span><br/>

<a NAME="E2:18"/><span class="kw">then </span>
(  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c2">g</font> &amp;  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c2">g</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c1">f</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="rfinseq2.html#E18"><span class="lab"><font color="Green" title="E5">Lm1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:18"/>
 <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rfinseq2.html#K3" title="RFINSEQ2:func.3">max</a> <font color="Maroon" title="c2">g</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</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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