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<span class="kw">set </span><font color="Maroon" title="c1">MS</font> =  <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a> ;<br/>
<span class="kw">let </span><font color="Maroon" title="c2">frequency</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="music_s1.html#D75" target="_self" onmouseover="rs('music_s1/D75')" onmouseout="rh()">MUSIC_S1:def 75</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a> st <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">frequency</font>,<font color="Olive" title="b1">q</font></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#K31" title="MUSIC_S1:func.31">fourth</a> <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c3">fr</font>, <font color="Maroon" title="c4">qr</font> being   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E2:162"/><span class="lab"><font color="Green" title="E104">A1</font></span>: 
<font color="Maroon" title="c3">fr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">frequency</font>
 <span class="kw">and </span><br/><a NAME="E3:162"/>
<font color="Maroon" title="c4">qr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">fr</font>
 <span class="kw">and </span><br/><a NAME="E4:162"/><span class="lab"><font color="Green" title="E105">A2</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">fr</font>,<font color="Maroon" title="c4">qr</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="music_s1.html#K31" title="MUSIC_S1:func.31">fourth</a> <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="music_s1.html#T96" target="_self" onmouseover="rs('music_s1/T96')" onmouseout="rh()">Th78</a></span>;<br/>
<a NAME="E5:162"/>
( <font color="Maroon" title="c3">fr</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a> &amp; <font color="Maroon" title="c4">qr</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="music_s1.html#T1" target="_self" onmouseover="rs('music_s1/T1')" onmouseout="rh()">Th1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:162"/>
 ex <font color="Olive" title="b1">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a> st <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">frequency</font>,<font color="Olive" title="b1">q</font></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#K31" title="MUSIC_S1:func.31">fourth</a> <a href="music_s1.html#K49" title="MUSIC_S1:func.49">REAL_Music</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:162"><span class="lab"><font color="Green" title="E104">A1</font></span></a>, <a class="txt" href="#E4:162"><span class="lab"><font color="Green" title="E105">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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