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

<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>

<b>assume </b><a NAME="E1:2_1_1"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c1">F</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>

<b>hence </b><a NAME="E2:2_1_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">x</font> is  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 <b>by </b><i><a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel27.html#D1" target="_self" title="WAYBEL27:def.1">WAYBEL27:def 1</a><br/>

<b>thus </b><a NAME="E3:2_1_1"/>
for <font color="Olive" title="b1">f</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_5.html#K4" title="FUNCT_5:func.4">uncurry</a> <font color="Olive" title="b1">f</font>
 <b>by </b><i><a class="txt" href="waybel27.html#E1:2_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>;<br/>

<b>thus </b><a NAME="E4:2_1_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font> holds <br/>( <font color="Olive" title="b1">x</font> is   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> &amp;  <a href="funct_5.html#K1" title="FUNCT_5:func.1">proj1</a> <font color="Olive" title="b1">x</font> is   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> )
 <b>by </b><i><a class="txt" href="waybel27.html#E1:2_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel27.html#D2" target="_self" title="WAYBEL27:def.2">WAYBEL27:def 2</a><br/>

<b>thus </b><a NAME="E5:2_1_1"/>
for <font color="Olive" title="b1">f</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_5.html#K3" title="FUNCT_5:func.3">curry</a> <font color="Olive" title="b1">f</font>
 <b>by </b><i><a class="txt" href="waybel27.html#E1:2_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>;<br/>

<b>thus </b><a NAME="E6:2_1_1"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">x</font> is  <a href="funcop_1.html#V1" title="FUNCOP_1:attr.1">Function-yielding</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>
 <b>by </b><i><a class="txt" href="waybel27.html#E1:2_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel27.html#D3" target="_self" title="WAYBEL27:def.3">WAYBEL27:def 3</a><br/>

<b>thus </b><a NAME="E7:2_1_1"/>
for <font color="Olive" title="b1">f</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Maroon" title="c1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="funct_6.html#K10" title="FUNCT_6:func.10">commute</a> <font color="Olive" title="b1">f</font>
 <b>by </b><i><a class="txt" href="waybel27.html#E1:2_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="relat_1.html#T60" title="RELAT_1:th.60">RELAT_1:60</a></i>;<br/>


</div>
