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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Tr2</font></span>: <a NAME="T9"><span class="comment"><font color="firebrick">:: DBLSEQ_2:9</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Rseq</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">n</font>, <font color="Olive" title="b3">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <span class="p1">(<span class="default"><a href="dblseq_2.html#K1" title="DBLSEQ_2:func.1">Partial_Sums_in_cod2</a> <font color="Olive" title="b1">Rseq</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">m</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="dblseq_2.html#K2" title="DBLSEQ_2:func.2">Partial_Sums_in_cod1</a> <span class="p2">(<span class="default"><a href="funct_4.html#K13" title="FUNCT_4:func.13">~</a> <font color="Olive" title="b1">Rseq</font></span>)</span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b2">n</font>) &amp; <span class="p1">(<span class="default"><a href="dblseq_2.html#K2" title="DBLSEQ_2:func.2">Partial_Sums_in_cod1</a> <font color="Olive" title="b1">Rseq</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">m</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="dblseq_2.html#K1" title="DBLSEQ_2:func.1">Partial_Sums_in_cod2</a> <span class="p2">(<span class="default"><a href="funct_4.html#K13" title="FUNCT_4:func.13">~</a> <font color="Olive" title="b1">Rseq</font></span>)</span></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b3">m</font>,<font color="Olive" title="b2">n</font>) )</div></div>
