<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.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"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><br/>

<a NAME="E1:79"/><span class="lab"><font color="Green" title="E59">A1</font></span>: 
 <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Olive" title="b1">z</font></span>)</span> where <font color="Olive" title="b1">z</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font> </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#D13" title="MEASURE6:def.13">MEASURE6:def 13</a></span>;<br/>
<a NAME="E2:79"/><span class="lab"><font color="Green" title="E60">A2</font></span>: 
 <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Olive" title="b1">z</font></span>)</span> where <font color="Olive" title="b1">z</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#D13" title="MEASURE6:def.13">MEASURE6:def 13</a></span>;<br/>
<a NAME="E3:79"/><span class="lab"><font color="Green" title="E61">A3</font></span>: 
<font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> ) </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#D23" title="SEQ_4:def.23">SEQ_4:def 23</a></span>;<br/>
<a NAME="E4:79"/><span class="lab"><font color="Green" title="E62">A4</font></span>: 
 <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Olive" title="b1">z</font></span>)</span> where <font color="Olive" title="b1">z</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#D13" title="MEASURE6:def.13">MEASURE6:def 13</a></span>;<br/>
<a NAME="E5:79"/><span class="lab"><font color="Green" title="E63">A5</font></span>: 
<span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Olive" title="b2">y</font></span>)</span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font> ) </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="seq_4.html#D23" title="SEQ_4:def.23">SEQ_4:def 23</a></span>;<br/>
<a NAME="E6:79"/>
for <font color="Olive" title="b1">z</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span> holds <br/><font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">z</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"> ( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span> implies <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:79_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</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">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">x</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E3:79_1"/><span class="lab"><font color="Green" title="E64">A6</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c4">x</font>
 <span class="kw">and </span><br/><a NAME="E4:79_1"/><span class="lab"><font color="Green" title="E65">A7</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E59">A1</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E6:79_1"/><span class="lab"><font color="Green" title="E66">A8</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">b</font>
 <span class="kw">and </span><br/><a NAME="E7:79_1"/><span class="lab"><font color="Green" title="E67">A9</font></span>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E8:79_1"/><span class="lab"><font color="Green" title="E68">A10</font></span>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79"><span class="lab"><font color="Green" title="E61">A3</font></span></a>, <a class="txt" href="#E4:79_1"><span class="lab"><font color="Green" title="E65">A7</font></span></a></span>;<br/>
<a NAME="E9:79_1"/><span class="lab"><font color="Green" title="E69">A11</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E60">A2</font></span></a>, <a class="txt" href="#E7:79_1"><span class="lab"><font color="Green" title="E67">A9</font></span></a></span>;<br/>
<a NAME="E10:79_1"/><span class="lab"><font color="Green" title="E70">A12</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:79"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="txt" href="#E8:79_1"><span class="lab"><font color="Green" title="E68">A10</font></span></a></span>;<br/>
<a NAME="E11:79_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c5">a</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c6">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79_1"><span class="lab"><font color="Green" title="E64">A6</font></span></a>, <a class="txt" href="#E6:79_1"><span class="lab"><font color="Green" title="E66">A8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:79_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:79"><span class="lab"><font color="Green" title="E63">A5</font></span></a>, <a class="txt" href="#E9:79_1"><span class="lab"><font color="Green" title="E69">A11</font></span></a>, <a class="txt" href="#E10:79_1"><span class="lab"><font color="Green" title="E70">A12</font></span></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><span class="kw">end;</span></div>
<a NAME="E7:79"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A13</font></span>: 
 <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T7" title="SUBSET_1:th.7">SUBSET_1:7</a></span>;<br/>
<a NAME="E8:79"/>
for <font color="Olive" title="b1">z</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span> holds <br/><font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="79_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">z</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"> ( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span> implies <font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:79_2"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</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">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E3:79_2"/><span class="lab"><font color="Green" title="E65">A14</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c5">y</font>
 <span class="kw">and </span><br/><a NAME="E4:79_2"/><span class="lab"><font color="Green" title="E66">A15</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">and </span><br/><a NAME="E5:79_2"/><span class="lab"><font color="Green" title="E67">A16</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:79"><span class="lab"><font color="Green" title="E63">A5</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">b</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E7:79_2"/><span class="lab"><font color="Green" title="E68">A17</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c6">b</font>
 <span class="kw">and </span><br/><a NAME="E8:79_2"/><span class="lab"><font color="Green" title="E69">A18</font></span>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:79"><span class="lab"><font color="Green" title="E62">A4</font></span></a>, <a class="txt" href="#E5:79_2"><span class="lab"><font color="Green" title="E67">A16</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">a</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><span class="kw"> such that </span><br/><a NAME="E10:79_2"/><span class="lab"><font color="Green" title="E70">A19</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">a</font>
 <span class="kw">and </span><br/><a NAME="E11:79_2"/><span class="lab"><font color="Green" title="E71">A20</font></span>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:79"><span class="lab"><font color="Green" title="E60">A2</font></span></a>, <a class="txt" href="#E4:79_2"><span class="lab"><font color="Green" title="E66">A15</font></span></a></span>;<br/>
<a NAME="E12:79_2"/><span class="lab"><font color="Green" title="E72">A21</font></span>: 
<font color="Maroon" title="c7">a</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79"><span class="lab"><font color="Green" title="E61">A3</font></span></a>, <a class="txt" href="#E11:79_2"><span class="lab"><font color="Green" title="E71">A20</font></span></a>, <a class="txt" href="#E8:79_2"><span class="lab"><font color="Green" title="E69">A18</font></span></a></span>;<br/>
<a NAME="E13:79_2"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">a</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c6">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79_2"><span class="lab"><font color="Green" title="E65">A14</font></span></a>, <a class="txt" href="#E10:79_2"><span class="lab"><font color="Green" title="E70">A19</font></span></a>, <a class="txt" href="#E7:79_2"><span class="lab"><font color="Green" title="E68">A17</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:79_2"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:79"><span class="lab"><font color="Green" title="E59">A1</font></span></a>, <a class="txt" href="#E12:79_2"><span class="lab"><font color="Green" title="E72">A21</font></span></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><span class="kw">end;</span></div>
<a NAME="E9:79"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T7" title="SUBSET_1:th.7">SUBSET_1:7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:79"/>
<span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <span class="p1">(<span class="default"><a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <font color="Maroon" title="c2">Y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure6.html#K4" title="MEASURE6:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="seq_4.html#K27" title="SEQ_4:func.27">+</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:79"><span class="lab"><font color="Green" title="E64">A13</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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>
