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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th6</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: MEASURE9:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">Y</font> being    <a href="finseq_2.html#M1" title="FINSEQ_2:mode.1">FinSequenceSet</a> of <font color="Olive" title="b1">D</font><br/>  for <font color="Olive" title="b3">F</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b2">Y</font><br/>  for <font color="Olive" title="b4">m1</font>, <font color="Olive" title="b5">m2</font>, <font color="Olive" title="b6">k1</font>, <font color="Olive" title="b7">k2</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">m1</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">m2</font> &amp; <font color="Olive" title="b4">m1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <span class="p2">(<span class="default"><a href="measure9.html#K2" title="MEASURE9:func.2">Length</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b6">k1</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">m2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <span class="p2">(<span class="default"><a href="measure9.html#K2" title="MEASURE9:func.2">Length</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b7">k2</font></span>)</span></span>)</span></span>)</span> &amp; <font color="Olive" title="b4">m1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <span class="p2">(<span class="default"><a href="measure9.html#K2" title="MEASURE9:func.2">Length</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b6">k1</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <span class="p1">(<span class="default"><a href="measure9.html#K2" title="MEASURE9:func.2">Length</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Olive" title="b6">k1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> &amp; <font color="Olive" title="b5">m2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <span class="p2">(<span class="default"><a href="measure9.html#K2" title="MEASURE9:func.2">Length</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b7">k2</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="wsierp_1.html#K1" title="WSIERP_1:func.1">Sum</a> <span class="p1">(<span class="default"><a href="measure9.html#K2" title="MEASURE9:func.2">Length</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">F</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><font color="Olive" title="b7">k2</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> holds <br/>( <font color="Olive" title="b4">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">m2</font> &amp; <font color="Olive" title="b6">k1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">k2</font> )</div></div>
