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<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: PRGCOR_2:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">b</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/>  for <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b1">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> &amp;  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">m</font> &amp; <font color="Olive" title="b1">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">m</font> holds <br/>(  ex <font color="Olive" title="b3">c</font> being   <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b2">m</font> <a href="prgcor_2.html#R3" title="PRGCOR_2:pred.3">vector_minus_prg</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">b</font> &amp; (  for <font color="Olive" title="b3">c</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="afinsq_1.html#NM2" title="AFINSQ_1:NM.2">XFinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>   st <font color="Olive" title="b2">m</font> <a href="prgcor_2.html#R3" title="PRGCOR_2:pred.3">vector_minus_prg</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">b</font> holds <br/> <a href="afinsq_1.html#K13" title="AFINSQ_1:func.13">XFS2FS*</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K6" title="RVSUM_1:func.6">-</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#K13" title="AFINSQ_1:func.13">XFS2FS*</a> <font color="Olive" title="b1">b</font></span>)</span> ) )</div></div>
