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<span class="kw">let </span><font color="Maroon" title="c3">L1</font>, <font color="Maroon" title="c4">L2</font> be   <a href="fdiff_1.html#NM2" title="FDIFF_1:NM.2">LINEAR</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">L2</font> is   <a href="fdiff_1.html#NM2" title="FDIFF_1:NM.2">LINEAR</a> &amp; <font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">L2</font> is   <a href="fdiff_1.html#NM2" title="FDIFF_1:NM.2">LINEAR</a> )</span><br/>



<span class="kw">consider </span><font color="Maroon" title="c5">g1</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E2:14"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
for <font color="Olive" title="b1">p</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds  <font color="Maroon" title="c3">L1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">g1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fdiff_1.html#D4" target="_self" title="FDIFF_1:def.4">Def4</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">g2</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E4:14"/><span class="lab"><font color="Green" title="E7">A2</font></span>: 
for <font color="Olive" title="b1">p</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds  <font color="Maroon" title="c4">L2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Olive" title="b1">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fdiff_1.html#D4" target="_self" title="FDIFF_1:def.4">Def4</a></span>;<br/>
<a NAME="E5:14"/><span class="lab"><font color="Green" title="E8">A3</font></span>: 
( <font color="Maroon" title="c3">L1</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp; <font color="Maroon" title="c4">L2</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="fdiff_1.html#D4" target="_self" title="FDIFF_1:def.4">Def4</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">p</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">g2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="rfunct_1.html#T72" title="RFUNCT_1:th.72">RFUNCT_1:72</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">g1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E6">A1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">g1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E7">A2</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">g1</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">g2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E7:14"/>
<font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Maroon" title="c4">L2</font> is   <a href="fdiff_1.html#NM2" title="FDIFF_1:NM.2">LINEAR</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="fdiff_1.html#D4" target="_self" title="FDIFF_1:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">L2</font> is   <a href="fdiff_1.html#NM2" title="FDIFF_1:NM.2">LINEAR</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">p</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c6">g2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">L2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">L1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="rfunct_1.html#T72" title="RFUNCT_1:th.72">RFUNCT_1:72</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">g1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">L2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c7">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E6">A1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">g1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g2</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E7">A2</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">g1</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c6">g2</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c7">p</font>

; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E9:14"/>
<font color="Maroon" title="c3">L1</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Maroon" title="c4">L2</font> is   <a href="fdiff_1.html#NM2" title="FDIFF_1:NM.2">LINEAR</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E8">A3</font></span></a>, <a class="ref" href="fdiff_1.html#D4" target="_self" title="FDIFF_1:def.4">Def4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
