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<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="valued_2.html#D28" target="_self" title="VALUED_2:def.28">VALUED_2:def 28</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_2.html#K18" title="VALUED_2:func.18">[+]</a> <font color="Maroon" title="c5">c</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_2.html#K18" title="VALUED_2:func.18">[+]</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> is  <a href="valued_0.html#V4" title="VALUED_0:attr.4">rational-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> )</span><br/>

<b>assume </b><a NAME="E1:149_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_2.html#K18" title="VALUED_2:func.18">[+]</a> <font color="Maroon" title="c5">c</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_2.html#K18" title="VALUED_2:func.18">[+]</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> is  <a href="valued_0.html#V4" title="VALUED_0:attr.4">rational-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a></span><br/>

<a NAME="E2:149_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_2.html#K18" title="VALUED_2:func.18">[+]</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="valued_1.html#K7" title="VALUED_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="valued_2.html#D36" target="_self" title="VALUED_2:def.36">Def36</a></i>;<br/>
<b>hence </b><a NAME="E3:149_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="valued_2.html#K18" title="VALUED_2:func.18">[+]</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> is  <a href="valued_0.html#V4" title="VALUED_0:attr.4">rational-valued</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 ; <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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