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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E47">Th44</font></span>: <a NAME="T44"><span class="comment"><font color="firebrick">:: NDIFF_5:44</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="prvect_2.html#NM3" title="PRVECT_2:NM.3">RealNormSpace-Sequence</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</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">G</font></span>)</span><br/>  for <font color="Olive" title="b4">Z</font>, <font color="Olive" title="b5">x0</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K15" title="PRVECT_1:func.15">carr</a> <font color="Olive" title="b1">G</font></span>)</span><br/>  for <font color="Olive" title="b6">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="prvect_2.html#K10" title="PRVECT_2:func.10">product</a> <font color="Olive" title="b1">G</font></span>)</span> &amp; <font color="Olive" title="b5">x0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> &amp; <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">Z</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">x0</font> <a href="card_3.html#K11" title="CARD_3:func.11">|</a> <font color="Olive" title="b6">X</font></span>)</span> holds <br/><span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b3">y</font></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"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b2">x</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span></div></div>
