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<span class="kw">reconsider </span><font color="Maroon" title="c4">g1</font> = <font color="Maroon" title="c2">f1</font>, <font color="Maroon" title="c5">g2</font> = <font color="Maroon" title="c3">f2</font> as   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="real_ns1.html#D4" onmouseover="rs('real_ns1/D4')" onmouseout="rh()">REAL_NS1:def 4</a></span>;<br/>
<a NAME="E2:50_1_1"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
( <font color="Maroon" title="c4">g1</font> is  <a href="nfcont_3.html#V2" title="NFCONT_3:attr.2">Lipschitzian</a>  &amp; <font color="Maroon" title="c5">g2</font> is  <a href="nfcont_3.html#V2" title="NFCONT_3:attr.2">Lipschitzian</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nfcont_4.html#T34" target="_self" onmouseover="rs('nfcont_4/T34')" onmouseout="rh()">Th34</a></span>;<br/>
<a NAME="E3:50_1_1"/>
<font color="Maroon" title="c4">g1</font> <a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">+</a> <font color="Maroon" title="c5">g2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="integr15.html#K7" title="INTEGR15:func.7">+</a> <font color="Maroon" title="c3">f2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nfcont_4.html#T5" target="_self" onmouseover="rs('nfcont_4/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:50_1_1"/>
 for <font color="Olive">b<sub>1</sub></font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<span class="p1">(<span class="default"><a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f1</font> <a href="integr15.html#K7" title="INTEGR15:func.7">+</a> <font color="Maroon" title="c3">f2</font> holds <br/><font color="Olive">b<sub>1</sub></font> is  <a href="nfcont_4.html#V2" title="NFCONT_4:attr.2">Lipschitzian</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></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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