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<div><span class="kw">theorem </span><a NAME="T33"><span class="comment"><font color="firebrick">:: MIDSP_3:33</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">m</font> being    <a href="midsp_3.html#M1" title="MIDSP_3:mode.1">Nat</a> of <font color="Olive" title="b1">n</font><br/>  for <font color="Olive" title="b3">RAS</font> being    <a href="midsp_3.html#M2" title="MIDSP_3:mode.2">ReperAlgebra</a> of <font color="Olive" title="b1">n</font><br/>  for <font color="Olive" title="b4">W</font> being   <a href="midsp_2.html#NM1" title="MIDSP_2:NM.1">ATLAS</a> of <font color="Olive" title="b3">RAS</font>  st <font color="Olive" title="b2">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> holds <br/>( <font color="Olive" title="b3">RAS</font> <a href="midsp_3.html#R4" title="MIDSP_3:pred.4">is_alternative_in</a> <font color="Olive" title="b2">m</font> iff  for <font color="Olive" title="b5">x</font> being   <a href="midsp_3.html#NM3" title="MIDSP_3:NM.3">Tuple</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Olive" title="b4">W</font> holds   <a href="midsp_3.html#K10" title="MIDSP_3:func.10">Phi</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">x</font> <a href="midsp_3.html#K1" title="MIDSP_3:func.1">+*</a> (<span class="p2">(<span class="default"><font color="Olive" title="b2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b5">x</font> <a href="midsp_3.html#K5" title="MIDSP_3:func.5">.</a> <font color="Olive" title="b2">m</font></span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="midsp_2.html#K11" title="MIDSP_2:func.11">0.</a> <font color="Olive" title="b4">W</font> )</div></div>
