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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th15</font></span>: <a NAME="T15"><span class="comment"><font color="firebrick">:: NDIFF_5:15</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">p</font>, <font color="Olive" title="b3">q</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">r0</font>, <font color="Olive" title="b5">p0</font>, <font color="Olive" title="b6">q0</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>  st <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">p0</font> &amp; <font color="Olive" title="b3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">q0</font> holds <br/>( <font color="Olive" title="b2">p</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b3">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">r0</font> iff  for <font color="Olive" title="b7">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">G</font> holds  <font color="Olive" title="b4">r0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">p0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b7">i</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">q0</font> <a href="ndiff_5.html#K1" title="NDIFF_5:func.1">.</a> <font color="Olive" title="b7">i</font></span>)</span> )</div></div>
