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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: CSSPACE4:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">seq1</font>, <font color="Olive" title="b2">seq2</font>, <font color="Olive" title="b3">seq3</font> being   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a> holds <br/> ( <font color="Olive" title="b1">seq1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">seq2</font> <a href="valued_1.html#K46" title="VALUED_1:func.46">-</a> <font color="Olive" title="b3">seq3</font> iff  for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Olive" title="b1">seq1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">seq2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">seq3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n</font></span>)</span> ) <span class="kw">by</span> <span class="lab"><a class="txt" href="csspace4.html#E18"><span class="lab"><font color="Green" title="E15">Lm11</font></span></a></span>;<br/></div></div>
