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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">LM01</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: LOPBAN11:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="prvect_2.html#NM3" title="PRVECT_2:NM.3">RealNormSpace-Sequence</a><br/>  for <font color="Olive" title="b2">Y</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="lopban10.html#NM2" title="LOPBAN10:NM.2">MultilinearOperator</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font><br/>  for <font color="Olive" title="b4">K</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">K</font> &amp; (  for <font color="Olive" title="b5">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Olive" title="b1">X</font></span>)</span> holds  <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="lopban10.html#K9" title="LOPBAN10:func.9">.</a> <font color="Olive" title="b5">x</font></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">K</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="lopban10.html#K11" title="LOPBAN10:func.11">NrProduct</a> <font color="Olive" title="b5">x</font></span>)</span> ) holds <br/> for <font color="Olive" title="b5">v0</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Olive" title="b1">X</font></span>)</span>  ex <font color="Olive" title="b6">M</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/>(  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b6">M</font> &amp; (  for <font color="Olive" title="b7">v1</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Olive" title="b1">X</font></span>)</span>  st <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b7">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b5">v0</font></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 holds <br/> ex <font color="Olive" title="b8">F</font> being    <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>  st <br/>(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b8">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">X</font> &amp; <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K10" title="FUNCT_2:func.10">/.</a> <font color="Olive" title="b7">v1</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K10" title="FUNCT_2:func.10">/.</a> <font color="Olive" title="b5">v0</font></span>)</span></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">M</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b4">K</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <font color="Olive" title="b8">F</font></span>)</span> &amp; (  for <font color="Olive" title="b9">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">X</font> holds  <font color="Olive" title="b8">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b9">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b7">v1</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b5">v0</font></span>)</span> <a href="lopban10.html#K10" title="LOPBAN10:func.10">.</a> <font color="Olive" title="b9">i</font></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> ) ) ) )</div></div>
