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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">LM84</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: DUALSP05:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">D</font> being    <a href="integra1.html#M1" title="INTEGRA1:mode.1">Division</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">m</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">A</font>,<span class="p1">(<span class="default"><a href="c0sp1.html#K6" title="C0SP1:func.6">BoundedFunctions</a> <font color="Olive" title="b1">A</font></span>)</span><br/>  for <font color="Olive" title="b4">rho</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ex <font color="Olive" title="b5">s</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="c0sp1.html#K11" title="C0SP1:func.11">R_Normed_Algebra_of_BoundedFunctions</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="dualsp05.html#K1" title="DUALSP05:func.1">ClstoCmp</a> <font color="Olive" title="b1">A</font></span>)</span></span>)</span> st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b5">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">D</font> &amp; (  for <font color="Olive" title="b6">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b6">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b5">s</font> holds <br/><font color="Olive" title="b5">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="absvalue.html#K1" title="ABSVALUE:func.1">sgn</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="dualsp05.html#K3" title="DUALSP05:func.3">Dp2</a> (<font color="Olive" title="b4">rho</font>,<font color="Olive" title="b2">D</font>,<span class="p4">(<span class="default"><font color="Olive" title="b6">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><a href="dualsp05.html#K3" title="DUALSP05:func.3">Dp2</a> (<font color="Olive" title="b4">rho</font>,<font color="Olive" title="b2">D</font>,<font color="Olive" title="b6">i</font>)</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="dualsp05.html#K2" title="DUALSP05:func.2">Dp1</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b2">D</font>,<span class="p3">(<span class="default"><font color="Olive" title="b6">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p2">(<span class="default"><a href="dualsp05.html#K2" title="DUALSP05:func.2">Dp1</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b2">D</font>,<font color="Olive" title="b6">i</font>)</span>)</span></span>)</span> ) )</div></div>
