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<span class="kw">let </span><font color="Maroon" title="c1">c</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</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"> ( <font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies  <a href="sin_cos.html#K23" title="SIN_COS:func.23">exp_R</a> <font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 )</span><br/>

<span class="kw">assume </span><a NAME="E1:3"/>
<font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</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">  <a href="sin_cos.html#K23" title="SIN_COS:func.23">exp_R</a> <font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1</span><br/>

<a NAME="E2:3"/><span class="kw">then </span>
(  <a href="sin_cos.html#K23" title="SIN_COS:func.23">exp_R</a> <font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 &amp;  <a href="sin_cos.html#K23" title="SIN_COS:func.23">exp_R</a> <font color="Maroon" title="c1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="sin_cos.html#T53" onmouseover="rs('sin_cos/T53')" onmouseout="rh()">SIN_COS:53</a>, <a class="ref" href="sin_cos7.html#T29" onmouseover="rs('sin_cos7/T29')" onmouseout="rh()">SIN_COS7:29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:3"/>
 <a href="sin_cos.html#K23" title="SIN_COS:func.23">exp_R</a> <font color="Maroon" title="c1">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</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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