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<span class="kw">let </span><font color="Maroon" title="c1">a</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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">  for <font color="Olive" title="b1">f</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b2">s</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b2">s</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Olive" title="b1">f</font> holds <br/> <a href="binpack1.html#K4" title="BINPACK1:func.4">SumBin</a> (<font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</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">  for <font color="Olive" title="b1">s</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">s</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f</font> holds <br/> <a href="binpack1.html#K4" title="BINPACK1:func.4">SumBin</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">f</font>,<font color="Olive" title="b1">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">s</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="c3">s</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f</font> implies  <a href="binpack1.html#K4" title="BINPACK1:func.4">SumBin</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:19"/><span class="lab"><font color="Green" title="E13">L033</font></span>: 
<font color="Maroon" title="c3">s</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c2">f</font>
 ; <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="binpack1.html#K4" title="BINPACK1:func.4">SumBin</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c4">emptyrealseq</font> =  <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> as    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/>
 <a href="binpack1.html#K3" title="BINPACK1:func.3">Seq</a> (<font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>) = 
 <a href="finseq_1.html#K15" title="FINSEQ_1:func.15">Seq</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span>)</span>

<br/>.= 
<font color="Maroon" title="c4">emptyrealseq</font>

;<br/>
<span class="kw">hence </span><a NAME="E4:19"/>
 <a href="binpack1.html#K4" title="BINPACK1:func.4">SumBin</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c3">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E13">L033</font></span></a>, <a class="ref" href="relat_1.html#T138" onmouseover="rs('relat_1/T138')" onmouseout="rh()">RELAT_1:138</a>, <a class="ref" href="rvsum_1.html#T72" onmouseover="rs('rvsum_1/T72')" onmouseout="rh()">RVSUM_1:72</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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