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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: MUSIC_S1:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">MS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="music_s1.html#V3" title="MUSIC_S1:attr.3">satisfying_equiv</a>   <a href="music_s1.html#V4" title="MUSIC_S1:attr.4">satisfying_interval</a>   <a href="music_s1.html#V7" title="MUSIC_S1:attr.7">satisfying_Nat</a>   <a href="music_s1.html#V8" title="MUSIC_S1:attr.8">satisfying_harmonic_closed</a>   <a href="music_s1.html#V11" title="MUSIC_S1:attr.11">satisfying_fifth_constructible</a>   <a href="music_s1.html#L1" title="MUSIC_S1:struct.1">MusicStruct</a> <br/>  for <font color="Olive" title="b2">frequency</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">MS</font>  ex <font color="Olive" title="b3">seq</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">MS</font> st <br/>( <font color="Olive" title="b3">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="ordinal1.html#K5" title="ORDINAL1:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">frequency</font> &amp; (  for <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">n</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">seq</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="music_s1.html#K30" title="MUSIC_S1:func.30">fifth</a> <font color="Olive" title="b1">MS</font> ) )</div></div>
