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

<span class="kw">set </span><font color="Maroon" title="c5">D</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span> ;<br/>
<div><span class="lab"><font color="Green" title="E2">A2</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:1_1_1_1_1"/>
( <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E3">A3</font></span>: 
<font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span>  is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><div class="add"><span class="kw">consider </span><font color="Maroon" title="c6">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>;<br/><font color="Maroon" title="c6">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  = 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 

<br/>.= 
<font color="Maroon" title="c4">yo</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_1_1_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a></span>
;<br/><a NAME="E4:1_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_1_1_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:1_1_1_1_1_1"/>
not <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span>  is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:1_1_1_1_1_2"/>
<font color="Maroon" title="c3">Bo</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span>  is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">b0</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E3">A4</font></span>: 
<font color="Maroon" title="c6">b0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Bo</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/><a NAME="E4:1_1_1_1_1_2"/>
<font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:1_1_1_1_1_2"><span class="lab"><font color="Green" title="E3">A4</font></span></a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></span>;<br/><a NAME="E5:1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E4">A5</font></span>: 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c7">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">yo</font>;<br/><a NAME="E6:1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E5">A6</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">yo</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">yo</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T18" title="FUNCT_4:th.18">FUNCT_4:18</a></span>;<br/><a NAME="E7:1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E6">A7</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">yo</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/><a NAME="E8:1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E7">A8</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">yo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Bo</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A9</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">yo</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">Bo</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></span>
<br/>.= 
<font color="Maroon" title="c2">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c3">Bo</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>
<br/>.= 
<font color="Maroon" title="c2">B</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1"><span class="lab"><font color="Green" title="E1">A1</font></span></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>
;<br/><a NAME="E10:1_1_1_1_1_2"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/><a NAME="E11:1_1_1_1_1_2"/><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="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:1_1_1_1_1_2"><span class="lab"><font color="Green" title="E4">A5</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E12:1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">yo</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:1_1_1_1_1_2"><span class="lab"><font color="Green" title="E6">A7</font></span></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">f</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">B</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">yo</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">b0</font></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c4">yo</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:1_1_1_1_1_2"><span class="lab"><font color="Green" title="E5">A6</font></span></a>, <a class="txt" href="#E9:1_1_1_1_1_2"><span class="lab"><font color="Green" title="E8">A9</font></span></a>, <a class="ref" href="funct_2.html#T4" title="FUNCT_2:th.4">FUNCT_2:4</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E14:1_1_1_1_1_2"/>
<font color="Maroon" title="c8">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:1_1_1_1_1_2"><span class="lab"><font color="Green" title="E7">A8</font></span></a>, <a class="ref" href="funct_4.html#T24" title="FUNCT_4:th.24">FUNCT_4:24</a></span>;<br/><a NAME="E15:1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span> 
 ;<br/><span class="kw">hence </span><a NAME="E16:1_1_1_1_1_2"/>
not <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span>  is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span>  implies <font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> )</span><br/><span class="kw">assume </span><a NAME="E1:1_1_1_2"/>
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</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="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span><br/><a NAME="E2:1_1_1_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">y</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> st <br/>( <font color="Maroon" title="c6">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> &amp; <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> )
 ;<br/><span class="kw">hence </span><a NAME="E3:1_1_1_2"/>
<font color="Maroon" title="c6">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</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>
<span class="kw">hence </span><a NAME="E3:1_1_1"/>
<span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font> : <font color="Olive" title="b1">y</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c3">Bo</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">yo</font> </span>}</span>  is  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c1">A</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:1_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</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>
