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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: SEQFUNC2:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">H</font> being   <a href="seqfunc.html#NM1" title="SEQFUNC:NM.1">Functional_Sequence</a> of <font color="Olive" title="b1">D</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">Y</font><br/>  for <font color="Olive" title="b4">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">D</font>  st <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b4">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="seqfunc.html#R1" title="SEQFUNC:pred.1">common_on_dom</a> <font color="Olive" title="b3">H</font> holds <br/>( <span class="p1"><a href="seqfunc2.html#K3" title="SEQFUNC2:func.3">||.</a><span class="default"><font color="Olive" title="b3">H</font></span><a href="seqfunc2.html#K3" title="SEQFUNC2:func.3">.||</a></span> <a href="seqfunc.html#K10" title="SEQFUNC:func.10">#</a> <font color="Olive" title="b4">x</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="normsp_0.html#K5" title="NORMSP_0:func.5">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">H</font> <a href="seqfunc2.html#K6" title="SEQFUNC2:func.6">#</a> <font color="Olive" title="b4">x</font></span>)</span></span><a href="normsp_0.html#K5" title="NORMSP_0:func.5">.||</a></span> &amp; <span class="p1">(<span class="default"><a href="seqfunc2.html#K2" title="SEQFUNC2:func.2">-</a> <font color="Olive" title="b3">H</font></span>)</span> <a href="seqfunc2.html#K6" title="SEQFUNC2:func.6">#</a> <font color="Olive" title="b4">x</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="seqfunc2.html#K6" title="SEQFUNC2:func.6">#</a> <font color="Olive" title="b4">x</font></span>)</span> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="seqfunc2.html#T19" target="_self" onmouseover="rs('seqfunc2/T19')" onmouseout="rh()">Th28</a></span>;<br/></div></div>
