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<span class="kw">let </span><font color="Maroon" title="c1">f</font> be   <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a>   <a href="partfun3.html#V1" title="PARTFUN3:attr.1">positive</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">  <a href="rvsum_3.html#K2" title="RVSUM_3:func.2">GMean</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_1.html#K3" title="FUNCT_1:func.3">the_value_of</a> <font color="Maroon" title="c1">f</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">v</font> =  <a href="funct_1.html#K3" title="FUNCT_1:func.3">the_value_of</a> <font color="Maroon" title="c1">f</font> as   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> ;<br/>
<a NAME="E2:21"/><span class="lab"><font color="Green" title="E10">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T14" onmouseover="rs('nat_1/T14')" onmouseout="rh()">NAT_1:14</a></span>;<br/>
<a NAME="E3:21"/><span class="lab"><font color="Green" title="E11">A4</font></span>: 
<font color="Maroon" title="c2">v</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_3.html#T10" target="_self" onmouseover="rs('rvsum_3/T10')" onmouseout="rh()">PosLeq</a></span>;<br/>
<a NAME="E4:21"/>
 <a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rvsum_3.html#T8" target="_self" onmouseover="rs('rvsum_3/T8')" onmouseout="rh()">ConstantProduct</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:21"/>
 <a href="rvsum_3.html#K2" title="RVSUM_3:func.2">GMean</a> <font color="Maroon" title="c1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_1.html#K3" title="FUNCT_1:func.3">the_value_of</a> <font color="Maroon" title="c1">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:21"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="txt" href="#E2:21"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="ref" href="power.html#T4" onmouseover="rs('power/T4')" onmouseout="rh()">POWER:4</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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