<?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="firebrick">::  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="member_1.html#K9" title="MEMBER_1:func.9">++</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="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><br/>

<a NAME="E1:72"/>
 for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</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="member_1.html#K9" title="MEMBER_1:func.9">++</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="72_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="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</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="member_1.html#K9" title="MEMBER_1:func.9">++</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="E1:72_1"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="member_1.html#K9" title="MEMBER_1:func.9">++</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">reconsider </span><font color="Maroon" title="c4">XY</font> = <font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font> as   <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="membered.html#T3" title="MEMBERED:th.3">MEMBERED:3</a></span>;<br/>
<a NAME="E3:72_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> <font color="Maroon" title="c4">XY</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72_1"><span class="lab"><font color="Green" title="E55">A1</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">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="E5:72_1"/><span class="lab"><font color="Green" title="E56">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">XY</font>
 <span class="kw">and </span><br/><a NAME="E6:72_1"/><span class="lab"><font color="Green" title="E57">A3</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="c5">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="measure6.html#T72" title="MEASURE6:th.72">MEASURE6:72</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">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="E8:72_1"/><span class="lab"><font color="Green" title="E58">A4</font></span>: 
<font color="Maroon" title="c6">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="E9:72_1"/><span class="lab"><font color="Green" title="E59">A5</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">and </span><br/><a NAME="E10:72_1"/><span class="lab"><font color="Green" title="E60">A6</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <font color="Maroon" title="c7">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:72_1"><span class="lab"><font color="Green" title="E56">A2</font></span></a>, <a class="ref" href="measure6.html#T21" title="MEASURE6:th.21">MEASURE6:21</a></span>;<br/>
<a NAME="E11:72_1"/><span class="lab"><font color="Green" title="E61">A7</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c6">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="#E8:72_1"><span class="lab"><font color="Green" title="E58">A4</font></span></a>, <a class="ref" href="member_1.html#T11" title="MEMBER_1:th.11">MEMBER_1:11</a></span>;<br/>
<a NAME="E12:72_1"/><span class="lab"><font color="Green" title="E62">A8</font></span>: 
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> <font color="Maroon" title="c7">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="#E9:72_1"><span class="lab"><font color="Green" title="E59">A5</font></span></a>, <a class="ref" href="member_1.html#T11" title="MEMBER_1:th.11">MEMBER_1:11</a></span>;<br/>
<a NAME="E13:72_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="c6">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="c7">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:72_1"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="txt" href="#E10:72_1"><span class="lab"><font color="Green" title="E60">A6</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:72_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="member_1.html#K9" title="MEMBER_1:func.9">++</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="#E11:72_1"><span class="lab"><font color="Green" title="E61">A7</font></span></a>, <a class="txt" href="#E12:72_1"><span class="lab"><font color="Green" title="E62">A8</font></span></a>, <a class="ref" href="member_1.html#T46" title="MEMBER_1:th.46">MEMBER_1:46</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/>


</div><span class="kw">end;</span></div>
<a NAME="E2:72"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A9</font></span>: 
 <a href="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</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="member_1.html#K9" title="MEMBER_1:func.9">++</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<a NAME="E3:72"/>
 for <font color="Olive" title="b1">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="member_1.html#K9" title="MEMBER_1:func.9">++</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="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_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="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="member_1.html#K9" title="MEMBER_1:func.9">++</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="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:72_2"/><span class="lab"><font color="Green" title="E56">A10</font></span>: 
<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="member_1.html#K9" title="MEMBER_1:func.9">++</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="firebrick">::  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="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font></span>)</span></span><br/>

<a NAME="E2:72_2"/>
<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="member_1.html#K9" title="MEMBER_1:func.9">++</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="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="membered.html#T3" title="MEMBERED:th.3">MEMBERED:3</a></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="E4:72_2"/><span class="lab"><font color="Green" title="E57">A11</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="E5:72_2"/><span class="lab"><font color="Green" title="E58">A12</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">and </span><br/><a NAME="E6:72_2"/><span class="lab"><font color="Green" title="E59">A13</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">by</span> <span class="lab"><a class="txt" href="#E1:72_2"><span class="lab"><font color="Green" title="E56">A10</font></span></a>, <a class="ref" href="measure6.html#T21" title="MEASURE6:th.21">MEASURE6:21</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="E8:72_2"/><span class="lab"><font color="Green" title="E60">A14</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">and </span><br/><a NAME="E9:72_2"/><span class="lab"><font color="Green" title="E61">A15</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">by</span> <span class="lab"><a class="txt" href="#E5:72_2"><span class="lab"><font color="Green" title="E58">A12</font></span></a>, <a class="ref" href="measure6.html#T72" title="MEASURE6:th.72">MEASURE6:72</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">X</font> = <font color="Maroon" title="c1">X</font> as   <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> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">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="E12:72_2"/><span class="lab"><font color="Green" title="E62">A16</font></span>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">X</font>
 <span class="kw">and </span><br/><a NAME="E13:72_2"/><span class="lab"><font color="Green" title="E63">A17</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="c8">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:72_2"><span class="lab"><font color="Green" title="E57">A11</font></span></a>, <a class="ref" href="measure6.html#T72" title="MEASURE6:th.72">MEASURE6:72</a></span>;<br/>
<a NAME="E14:72_2"/><span class="lab"><font color="Green" title="E64">A18</font></span>: 
<font color="Maroon" title="c8">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="c7">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:72_2"><span class="lab"><font color="Green" title="E62">A16</font></span></a>, <a class="txt" href="#E8:72_2"><span class="lab"><font color="Green" title="E60">A14</font></span></a>, <a class="ref" href="member_1.html#T46" title="MEMBER_1:th.46">MEMBER_1:46</a></span>;<br/>
<a NAME="E15:72_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="c8">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="#E6:72_2"><span class="lab"><font color="Green" title="E59">A13</font></span></a>, <a class="txt" href="#E13:72_2"><span class="lab"><font color="Green" title="E63">A17</font></span></a>, <a class="txt" href="#E9:72_2"><span class="lab"><font color="Green" title="E61">A15</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:72_2"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:72_2"><span class="lab"><font color="Green" title="E64">A18</font></span></a>, <a class="ref" href="member_1.html#T11" title="MEMBER_1:th.11">MEMBER_1:11</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/>


</div><span class="kw">end;</span></div>
<a NAME="E4:72"/><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="member_1.html#K9" title="MEMBER_1:func.9">++</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="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:72"/>
<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="member_1.html#K9" title="MEMBER_1:func.9">++</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="member_1.html#K5" title="MEMBER_1:func.5">--</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="member_1.html#K9" title="MEMBER_1:func.9">++</a> <font color="Maroon" title="c2">Y</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:72"><span class="lab"><font color="Green" title="E55">A9</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="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
