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<b>set </b><font color="Maroon" title="c1">f</font> = <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="relset_1.html#K8" title="RELSET_1:func.8">|</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#K36" title="SIN_COS:func.36">PI</a> </span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>;<br/>
<a NAME="E1:99"/><i><font color="Green" title="E94">A1</font></i>: 
<span class="p1">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="relset_1.html#K8" title="RELSET_1:func.8">|</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#K36" title="SIN_COS:func.36">PI</a> </span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</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#K36" title="SIN_COS:func.36">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>
 
<b>by </b><i><a class="ref" href="sin_cos6.html#T49" target="_self" title="SIN_COS6:th.49">Th49</a>, <a class="ref" href="relat_1.html#T162" title="RELAT_1:th.162">RELAT_1:162</a></i>;<br/>
<a NAME="E2:99"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="relset_1.html#K8" title="RELSET_1:func.8">|</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#K36" title="SIN_COS:func.36">PI</a> </span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</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#K36" title="SIN_COS:func.36">PI</a> </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>
 
<b>by </b><i><a class="ref" href="comptrig.html#T41" title="COMPTRIG:th.41">COMPTRIG:41</a></i>;<br/>
<a NAME="E3:99"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="relset_1.html#K8" title="RELSET_1:func.8">|</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#K36" title="SIN_COS:func.36">PI</a> </span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">|</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#K36" title="SIN_COS:func.36">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#K8" title="RELSET_1:func.8">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a>  <a href="relset_1.html#K8" title="RELSET_1:func.8">|</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#K36" title="SIN_COS:func.36">PI</a> </span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span></span>)</span> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</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#K36" title="SIN_COS:func.36">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>
 
<b>by </b><i><a class="ref" href="fcont_3.html#T18" title="FCONT_3:th.18">FCONT_3:18</a></i>;<br/>
<b>hence </b><a NAME="E4:99"/>
<a href="sin_cos6.html#K4" title="SIN_COS6:func.4">arccos</a>  <a href="relset_1.html#K8" title="RELSET_1:func.8">|</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>
 <b>by </b><i><a class="txt" href="#E1:99"><i><font color="Green" title="E94">A1</font></i></a>, <a class="ref" href="relat_1.html#T101" title="RELAT_1:th.101">RELAT_1:101</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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