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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E33">SH4</font></span>: <a NAME="T48"><span class="comment"><font color="firebrick">:: DBLSEQ_2:48</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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">s</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <font color="Olive" title="b1">X</font> holds <br/> (  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K6" title="ORDINAL1:func.6">Segm</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K6" title="ORDINAL1:func.6">Segm</a> 1</span>)</span></span>)</span>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> &amp;  <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K6" title="ORDINAL1:func.6">Segm</a> 2</span>)</span></span>)</span>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> 1</span>)</span></span><a href="finseq_1.html#K10" title="FINSEQ_1:func.10">*&gt;</a></span> &amp; (  for <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds   <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">s</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K6" title="ORDINAL1:func.6">Segm</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>,1) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p3">(<span class="default"><a href="ordinal1.html#K6" title="ORDINAL1:func.6">Segm</a> <font color="Olive" title="b3">n</font></span>)</span></span>)</span>,1)</span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1"><a href="matrix_0.html#K13" title="MATRIX_0:func.13">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">s</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">n</font></span>)</span></span><a href="matrix_0.html#K13" title="MATRIX_0:func.13">*&gt;</a></span> ) )</div></div>
