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<a NAME="E1:14_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">rf</font> <a href="finseq_3.html#K1" title="FINSEQ_3:func.1">-</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rvsum_1.html#K1" title="RVSUM_1:func.1">rng</a> <font color="Maroon" title="c1">rf</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_3.html#T66" title="FINSEQ_3:th.66">FINSEQ_3:66</a></span>;<br/>
<a NAME="E2:14_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">rf</font> <a href="finseq_3.html#K1" title="FINSEQ_3:func.1">-</a> <font color="Maroon" title="c2">X</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1"/>
<font color="Maroon" title="c1">rf</font> <a href="finseq_3.html#K1" title="FINSEQ_3:func.1">-</a> <font color="Maroon" title="c2">X</font> is  <a href="valued_0.html#V3" title="VALUED_0:attr.3">real-valued</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="valued_0.html#D3" title="VALUED_0:def.3">VALUED_0:def 3</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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