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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="integra1.html#V1" title="INTEGRA1:attr.1">closed-interval</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">A</font> <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"><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> implies  <a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a>  <a href="integra9.html#R1" title="INTEGRA9:pred.1">is_orthogonal_with</a>  <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> ,<font color="Maroon" title="c1">A</font> )</span><br/>

<b>assume </b><a NAME="E1:40"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c1">A</font> <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"><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 class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a>  <a href="integra9.html#R1" title="INTEGRA9:pred.1">is_orthogonal_with</a>  <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> ,<font color="Maroon" title="c1">A</font></span><br/>

<a NAME="E2:40"/>
<span class="p1"><a href="integra9.html#K1" title="INTEGRA9:func.1">|||(</a><span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> ,<a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> ,<font color="Maroon" title="c1">A</font></span><a href="integra9.html#K1" title="INTEGRA9:func.1">)|||</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="integra8.html#T92" title="INTEGRA8:th.92">INTEGRA8:92</a>, <a class="txt" href="#E1:40"><i><font color="Green" title="E22">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:40"/>
 <a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a>  <a href="integra9.html#R1" title="INTEGRA9:pred.1">is_orthogonal_with</a>  <a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> ,<font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="integra9.html#D2" target="_self" title="INTEGRA9:def.2">Def2</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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