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<span class="kw">set </span><font color="Maroon" title="c1">f</font> = <a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>;<br/>
<a NAME="E1:99"/>
( <span class="p1">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p4"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="partfun2.html#K2" title="PARTFUN2:func.2">"</a></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">cos</a> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p3"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p2"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="sin_cos.html#K33" title="SIN_COS:func.33">PI</a></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> is  <a href="valued_0.html#V8" title="VALUED_0:attr.8">decreasing</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos6.html#T49" target="_self" title="SIN_COS6:th.49">Th49</a>, <a class="ref" href="comptrig.html#T25" title="COMPTRIG:th.25">COMPTRIG:25</a>, <a class="ref" href="fcont_3.html#T10" title="FCONT_3:th.10">FCONT_3:10</a>, <a class="ref" href="relat_1.html#T129" title="RELAT_1:th.129">RELAT_1:129</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:99"/>
<a href="sin_cos6.html#K4" title="SIN_COS6:func.4">arccos</a> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> is  <a href="valued_0.html#V8" title="VALUED_0:attr.8">decreasing</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T72" title="RELAT_1:th.72">RELAT_1:72</a></span>; <a class="txt" 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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